ORIGINAL_ARTICLE
On exponentiable soft topological spaces
An object $X$ of a category $\mathbf{C}$ with finite limits is called exponentiable if the functor $-\times X:\mathbf{C}\rightarrow \mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable spaces in the category $\mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $\mathbf{STop}$ of soft topological spaces which is a generalization of the category $\mathbf{Top}$. We investigate the exponentiability problem and give a characterization of exponentiable soft spaces. Also wegive the definition of exponential topology on the lattice of soft open sets of a soft space and present some characterizations of it.
https://scma.maragheh.ac.ir/article_22216_6c2f05eb0b9ad6ca148f19bd3ef7cb1d.pdf
2016-11-01
1
14
Soft set theory
Soft topology
Exponentiable object
Ghasem
Mirhosseinkhani
gh.mirhosseini@yahoo.com
1
Department of Mathematics, Sirjan University of Technology, Sirjan, Iran.
LEAD_AUTHOR
Ahmad
Mohammadhasani
a.mohammadhasani@sirjantech.ac.ir
2
Department of Mathematics, Sirjan University of Technology, Sirjan, Iran.
AUTHOR
[1] J. Adamek, H. Herrlich, and G.E. Strecker, Abstract and concrete categories, John Wiely and Sons Inc., New York, 1990.
1
[2] H. Akta¸s and N. Cagman, Soft sets and soft groups, Inform. Sci., 177 (2007) 2726-2735.
2
[3] A. Aygunoglu and H. Aygun, Some notes on soft topological spaces, Neural. Comput. Appl., 21 (2011) 113-119.
3
[4] N. Cagman and S. Enginoglu, Soft set theory and uni-int decision making, European J. Oper. Res., 207 (2010) 848-855.
4
[5] N. Ca¢gman and S. Enginoglu, Soft matrix theory and its decision making, Comput. Math. Appl., {59} (2010) 3308-3314.
5
[6] N. Ca¢gman, S. Karata¸s and S. Enginoglu, Soft topology, Comput. Math. Appl., 62 (2011) 351-358.
6
[7] M.H. Escard´o and R. Heckmann, Topologies on spaces of continuous functions, Topology Proc., 26(2) (2001-2002) 545-564.
7
[8] M.H. Escardo, J. Lawson, and A. Simpson, Comparing Cartesian closed categories of (core) compactly generated spaces, Topology Appl., 143 (2004) 105-145.
8
[9] F. Feng, Y.B. Jun, and X. Zhao, Soft semirings, Comput. Math. Appl., 56(10) (2008) 2621-2628.
9
[10] N. Georgiou and A.C. Megaritis, Soft set theory and topology, Appl. Gen. Topol., 15(1) (2014) 93-109.
10
[11] N. Georgiou, A.C. Megaritis, and V.I. Petropoulos, On soft topological spaces, Appl. Math. Inf. Sci., 7(5) (2013) 1889-1901.
11
[12] G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott, Continuous Lattices and Domains, Cambridge University Press, 2003.
12
[13] S. Hussain and B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl., {62} (2011) 4058-4067.
13
[14] O. Kazanci, S. Yilmaz, and S. Yamak, Soft Sets and Soft BCH-Algebras, Hacet. J. Math. Stat., 39(2) (2010) 205-217.
14
[15] P.K. Maji, A.R. Roy, and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002) 1077-1083.
15
[16] W.K. Min, A note on soft topological spaces, Comput. Math. Appl., 62 (2011) 3524-3528.
16
[17] D.A. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999) 19-31.
17
[18] D.A. Molodtsov, The description of a dependence with the help of soft sets, J. Comput. Syst. Sci. Int., 40(6) (2001) 977-984.
18
[19] D.A. Molodtsov, The theory of soft sets (in Russian), URSS Publishers, Moscow, 2004.
19
[20] D.A. Molodtsov, V.Y. Leonov, and D.V. Kovkov, Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 1(1) (2006) 8-39.
20
[21] D. Pei and D. Miao, From soft sets to information systems, In: X. Hu, Q. Liu, A. Skowron, T.Y. Lin, R.R. Yager, B. Zhang, eds., Proceedings of Granular Computing, IEEE, 2 (2005) 617-621.
21
[22] M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (2011) 1786-1799.
22
[23] Y. Shao and K. Qin, The lattice structure of the soft groups, Procedia Engineering, 15 (2011) 3621-3625.
23
[24] I. Zorlutuna, M. Akdag, W.K. Min, and S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 3(2) (2012) 171-185.
24
[25] Y. Zou and Z. Xiao, Data analysis approaches of soft sets under incomplete information, Knowl. Base. Syst., 21 (2008) 941-945.
25
ORIGINAL_ARTICLE
A spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems
In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature formula to reduce the fractional optimal control problem to solving a system of nonlinear algebraic equations that greatly simplifies the problem. Finally, some examples are included to confirm the efficiency and accuracy of the proposed method.
https://scma.maragheh.ac.ir/article_20586_9a66f07fa643034de1eac90f764c105c.pdf
2016-11-01
15
27
Fractional optimal control problems
Caputo fractional derivative
Riemann-Liouville fractional integral
Second-kind Chebyshev polynomials
Operational matrix
Somayeh
Nemati
s.nemati@umz.ac.ir
1
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
LEAD_AUTHOR
[1] O.M.P. Agrawal, A general formulation and solution scheme for fractional optimal control problem, Nonlinear Dynam., 38 (2004) 323-337.
1
[2] O.M.P. Agrawal, A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems, J. Vib. Control, (2007) 1269-1281.
2
[3] O.M.P. Agrawal, A formulation and numerical scheme for fractional optimal control problems, J. Vib. Control, 14 (2008) 1291-1299.
3
[4] R.L. Bagley and P.J. Torvik, A theoretical basis for the application of fractional calculus to viscoelasticity, J. Rheol., 27 (1983) 201--210.
4
[5] R.L. Bagley and P.J. Torvik, Fractional calculus in the transient analysis of viscoelastically damped structures, AIAA J., 23 (1985) 918-925.
5
[6] D. Baleanu, O. Defterli, and O.M.P. Agrawal, A central difference numerical scheme for fractional optimal control problems, J. Vib. Control, 15 (2009) 547-597.
6
[7] G. Bohannan, Analog fractional order controller in temperature and motor control applications, J. Vibr. Control, 14 (2008) 1487-1498.
7
[8] K.B. Datta and B.M. Mohan, Orthogonal Functions in Systems and Control, World Scientific, Singapore, 1995.
8
[9] R.A. Devore and L.R. Scott, Error bounds for Gaussian quadrature and weighted-L1 polynomial approximation, SIAM J. Numer. Anal., 21 (1984) 400-412.
9
[10] K. Diethelm and N.J. Ford, Multi-order fractional differential equations and their numerical solution, Appl. Math. Comput., 154 (2004) 621--640.
10
[11] W. Grzesikiewicz, A. Wakulicz, and A. Zbiciak, Non-linear problems of fractional in modelling of mechanical systems, Int. J. Mech. Sci., 70 (2013) 90-89.
11
[12] J.H. He, Some applications of nonlinear fractional differential equations and their applications, Bull. Sci. Technol., 15 (1999) 86-90.
12
[13] M. Ichise,Y. Nagayanagi, and T. Kojima, An analog simulation of noninteger order transfer functions for analysis of electrode process, J. Electroanal. Chem., 33 (1971) 253-265.
13
[14] H. Jafari, and H. Tajadodi, Fractional order optimal control problems via the operational matrices of Bernstein polynomials, U.P.B. Sci. Bull., Series A, 76(3) (2014) 115-128.
14
[15] Y. Jiang, X. Wang, and Y. Wang, On a stochastic heat equation with first order fractional noises and applications to finance, J. Math. Anal, Appl., 396 (2012) 656-669.
15
[16] E. Keshavarz, Y. Ordokhani, and M. Razzaghi, A numerical solution for fractional optimal control problems via Bernoulli polynomials, J. Vib. Control, 29 (2015) 1-15.
16
[17] R. Lewandowski, and B. Chorazyczewski, Identification of the parameters of the Kelvin-Voigt and the Maxwell fractional models, used to modeling of viscoelastic dampers, Comput. Struct., 88 (2010) 1-17.
17
[18] A. Lotfi, M. Dehghan, and S.A. Yousefi, A numerical technique for solving fractional optimal control problems, Comput. Math. Appl., 62 (2011) 1055-1067.
18
[19] A. Lotfi, S.A. Yousefi, and Mehdi Dehghanb, Numerical solution of a class of fractional optimal control problems via the Legendre orthonormal basis combined with the operational matrix and the Gauss quadrature rule, J. Comput. Appl. Math., 250 (2013) 143-160
19
[20] R.L. Magin, Fractional calculus in bioengineering, Crit. Rev. Biomed. Eng., 32 (2004) 1-104.
20
[21] F. Mainardi, Fractional calculus: some basic problems in continuum and statistical mechanics, Fract. Fract. Calculus Contin. Mech., 387 (1997) 291--348.
21
[22] Y.A. Rossikhin and M.V. Shitikova, Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids, Appl. Mech. Rev., 50 (1997) 15-67.
22
[23] N. Sebaa, Z.E.A. Fellah, W. Lauriks, and C. Depollier, Application of fractional calculus to ultrasonic wave propagation in human cancellous bone, Signal Process., 86 (2006) 2668-2677.
23
[24] V.E. Tarasov, Fractional vector calculus and fractional Maxwells equations, Annals of Physics, 323 (2008) 2756-2778.
24
[25] J.A. Tenreiro Machado, P. Stefanescu, O. Tintareanu, and D. Baleanu, Fractional calculus analysis of the cosmic microwave background, Rom. Rep. Phys., 65 (2013) 316-323.
25
[26] E. Tohidi and H. Saberi Nik, A Bessel collocation method for solving fractional optimal control problems, Appl. Math. Model., 39(2) (2015) 455-465.
26
[27] C. Tricaud and Y.Q. Chen, An approximation method for numerically solving fractional order optimal control problems of general form, Comput. Math. Appl., 59 (2010) 1644-1655.
27
[28] S.A. Yousefi, A. Lotfi, and M. Dehghan, The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems, J. Vib. Control, 13 (2011) 1-7.
28
[29] S.B. Yuste, L. Acedo, and K. Lindenberg, Reaction front in an A + B → C reaction-subdiffusion process, Phys. Rev. E., 69 (2004) 036126.
29
ORIGINAL_ARTICLE
Convergence analysis of the sinc collocation method for integro-differential equations system
In this paper, a numerical solution for a system of linear Fredholm integro-differential equations by means of the sinc method is considered. This approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. The exponential convergence rate $O(e^{-k \sqrt{N}})$ of the method is proved. The analytical results are illustrated with numerical examples that exhibit the exponential convergence rate.
https://scma.maragheh.ac.ir/article_20588_07e309a824a67c1d2a2ed35788e411f9.pdf
2016-11-01
29
42
Fredholm integro-differential
System of equation
Sinc function
Convergence
Mohammad
Zarebnia
zarebnia@uma.ac.ir
1
Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili,m, P.O.Box 56199-11367, Ardabil, Iran.
LEAD_AUTHOR
[1] A. Akyuz-Dacslcouglu and M. Sezer, Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations, Journal of the Franklin Institute, 342 (2005) 688-701.
1
[2] A. Arikoglu and I. Ozkol, Solutions of integral and integro-differential equation systems by using differential transform method, Computers and Mathematics with Applications, 56 (2008) 2411-2417.
2
[3] N. Eggert, M. Jarratt, and J. Lund, Sinc function computations of the eigenvalues of Strum-Lioville problems, J. Comput. Phys., 69 (1987) 209-229.
3
[4] J. Lund and K. Bowers, Sinc Methods For Quadrature and Differential Equations, SIAM, Philadelphia, PA, 1992.
4
[5] J. Lund and C. Vogel, A Fully-Galerkin method for the solution of an inverse problem in a parabolic partial differential equation. numerical solution of an inverse, Inverse Problems, 6 (1990) 205-217.
5
[6] J. Lund and B.V. Rilay, A Sinc-collocation method for the computation of the eigenvalues of the radial Schrodinger equation, IMA J. Numer. Anal., 4 (1984) 83-98.
6
[7] I. Patlashenko, D. Givoli, and P. Barbone, Time-stepping schemes for system of Volterra integro-differential equations, Comput. Methods Appl. Mech. Engrg., 190 (2001) 5691-5718.
7
[8] J. Rashidinia and M. Zarebnia, Convergence of approximate solution of system of Fredholm integral equations, J. Math. Anal. Appl. 333 (2007) 1216--1227.
8
[9] R. Smith and K. Bowers, A Sinc-Galerkin estimation of diffusivity in parabolic problems, Inverse Problems, 9 (1993) 113-135.
9
[10] F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer-Verlag, New York, 1993.
10
[11] E. Yusufouglu, Numerical solving initial value problem for Fredholm type linear integro-differential equation system,
11
Journal of the Franklin Institute, 346 (2009) 636--649.
12
[12] E. Yusufouglu, An efficient algorithm for solving integro-differential equations system, Applied Mathematics and Computation, 192 (2007) 51-55.
13
ORIGINAL_ARTICLE
Construction of continuous $g$-frames and continuous fusion frames
A generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by M. H. Faroughi and R. Ahmadi, is presented in this study. Continuous resolution of the identity (CRI) is introduced, a new family of CRI is constructed, and a number of reconstruction formulas are obtained. Also, new results are given on the duality of continuous fusion frames in Hilbert spaces.
https://scma.maragheh.ac.ir/article_22217_ae4c4518ab8f84876feb316820fad8b5.pdf
2016-11-01
43
55
Fusion frame
Continuous fusion frame
Continuous $g$-frame
Continuous resolution
Mahdiyeh
Khayyami
mahdiyehkhayyami@yahoo.com
1
Department of Mathematics, Science and Research Branch, Islamic Azad University, Kerman, Iran.
AUTHOR
Akbar
Nazari
nazari@mail.uk.ac.ir
2
Department of Mathematics, Science and Research Branch, Islamic Azad University, Kerman, Iran.
LEAD_AUTHOR
[1] M.R. Abdollahpour and M.H. Faroughi, Continuous $g$-frames in Hilbert spaces, Southeast Asian Bull. Math., 32, 1-19(2008).
1
[2] S.T. Ali, J.P. Antoine, and J.P Gazeau, Continuous frames in Hilbert spaces, Annals of Physics. 222, 1-37 (1993).
2
[3] M.S. Asgari and A. Khosravi, Frames and bases of subspaces in Hilbert spaces, J. Math. Anal. Appl., 308, 541-553 (2005).
3
[4] O. Christensen, An introduction to frame and Riesz bases, Birkhäuser, Boston, 2003.
4
[5] I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27, 1271-1283 (1986).
5
[6] I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF conference series in applied mathematics, 61, SIAM, Philadelphia, 1992.
6
[7] R. Duffin and A. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72, 341-366 (1952).
7
[8] M.H. Faroughi and R. Ahmadi, Fusion integral, J. Mathematische Nachrichten. 284, No. 5-6, 681-693 (2011).
8
[9] M.H. Faroughi and R. Ahmadi, Some properties of $C$-fusion frames, Turk J Math., 34, 393-415. (2010).
9
[10] J.P. Gabardo and D. Han, Frames Associated with Measurable Space, Adv. Comp. Math., 18, 127-147 (2003).
10
[11] P. Gavruta, On the duality of fusion frames in Hilbert spaces, J. Math. Anal. Appl., 333, 871-879 (2007).
11
[12] G. Kaiser, A Friendly Guide to Wavelets, Birkhäuser, 1994.
12
[13] A. Khosravi and K. Musazadeh, Fusion frames and $g$-frames, J. Math. Anal. Appl., 342, 1068-1083 (2008).
13
[14] W. Sun, $g$-frame and $g$- Riesz bases, J. Math. Anal. Appl., 322, 437-452 (2006).
14
ORIGINAL_ARTICLE
Solution of nonlinear Volterra-Hammerstein integral equations using alternative Legendre collocation method
Alternative Legendre polynomials (ALPs) are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given and the efficiency and accuracy are illustrated by applying the method to some examples.
https://scma.maragheh.ac.ir/article_22018_9e7878429e482a2594ae157e2e39fd77.pdf
2016-11-01
57
77
Nonlinear Volterra-Hammerstein integral equations
Alternative Legendre polynomials
Operational matrix
Collocation method
Sohrab
Bazm
sbazm@maragheh.ac.ir
1
Department of Mathematics, Faculty of Science, University of Maragheh,, P.O.Box 55181-83111 Maragheh, Iran.
LEAD_AUTHOR
[1] I. Aziz and Siraj-ul-Islam, New algorithms for the numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets, J. Comput. Appl. Math. 239 (2013) 333-345.
1
[2] H. O. Bakodah and M. A. Darwish, On discrete Adomian decomposition method with Chebyshev abscissa for nonlinear integral equations of Hammerstein type, Adv. Pure Math. 2 (2012) 310-313.
2
[3] S. Bazm, Bernoulli polynomials for the numerical solution of some classes of linear and nonlinear integral equations, J. Comput. Appl. Math. 275 (2015) 44-60.
3
[4] H. Brunner, On the numerical solution of nonlinear Volterra-Fredholm integral equation by collocation methods, SIAM J. Numer. Anal. 27 (1990) 987-1000.
4
[5] H. Brunner and N. Yan, On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations, J. Comput. Appl. Math. 67(1) (1996) 185-189.
5
[6] V. S. Chelyshkov, Alternative Orthogonal Polynomials and Quadratures, Electron. Trans. Numer. Anal. 25(7) (2006) 17-26.
6
[7] V. S. Chelyshkov, Alternative Jacobi polynomials and orthogonal exponentials, arXiv:1105.1838.
7
[8] M. A. Darwish, Fredholm-Volterra integral equation with singular kernel, Korean J. Comput. Appl. Math. 6 (1999) 163-174.
8
[9] M. A. Darwish, Note on stability theorems for nonlinear mixed integral equations, J. Appl. Math. Comput. 6 (1999) 633-637.
9
[10] F. Deutsch, Best approximation in inner product spaces, Springer-Verlag, New York, 2001.
10
[11] M. Gasca and T. Sauer, On the history of multivariate polynomial interpolation, J. Comput. Appl. Math. 122 (2000) 23-35.
11
[12] A. Gil, J. Segura and N. M. Temme, Numerical methods for special functions, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2007.
12
[13] E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, 1989.
13
[14] K. Maleknejad, H. Almasieh, and M. Roodaki, Triangular functions (TF) method for the solution of nonlinear Volterra-Fredholm integral equations, Commun. Nonlinear Sci. Numer. Simul. 15(11) (2010) 3293-3298.
14
[15] K. Maleknejad, E. Hashemizadeh, and B. Basirat, Computational method based on Bernstein operational matrices for nonlinear Volterra-Fredholm-Hammerstein integral equations, Commun. Nonlinear Sci. Numer. Simul. 17(1) (2012) 52-61.
15
[16] S. Nemati, P.M. Lima, and Y. Ordokhani, Numerical solution of a class of two-dimensional nonlinear Volterra integral equations using Legendre polynomials, J. Comput. Appl. Math. 242 (2013) 53-69.
16
[17] H. Li and H. Zou, A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations, J. Comput. Appl. Math. 237(1) (2013) 35-42.
17
[18] B. G. Pachpatte, On a nonlinear Volterra-Fredholm integral equation, Sarajevo J. Math. 16 (2008) 61-71.
18
[19] I. Singh and S. Kumar, Haar wavelet method for some nonlinear Volterra integral equations of the first kind, J. Comput. Appl. Math. 292 (2016) 541-552.
19
[20] G. Szego, Orthogonal Polynomials, AMS, Providence, 1975.
20
[21] A. M. Wazwaz, A reliable treatment for mixed Volterra-Fredholm integral equations, Appl. Math. Comput. 127 (2002) 405-414.
21
[22] C. Yang, Chebyshev polynomial solution of nonlinear integral equations, Journal of the Franklin Institute, 349 (2012) 947-956.
22
ORIGINAL_ARTICLE
On isomorphism of two bases in Morrey-Lebesgue type spaces
Double system of exponents with complex-valued coefficients is considered. Under some conditions on the coefficients, we prove that if this system forms a basis for the Morrey-Lebesgue type space on $\left[-\pi , \pi \right]$, then it is isomorphic to the classical system of exponents in this space.
https://scma.maragheh.ac.ir/article_22226_0b34cf5e5a4f7c322ff3393fa083fff2.pdf
2016-11-01
79
90
Morrey-Lebesgue type space
System of exponents
Isomorphism
Basicity
Fatima. A.
Guliyeva
quliyeva-fatima@mail.ru
1
Institute of Mathematics and Mechanics of NAS of Azerbaijan, Az1141, Baku, Azerbaijan.
LEAD_AUTHOR
Rubaba H.
Abdullayeva
rubab.aliyeva.ra@gmail.com
2
Math teacher at the school No 297, Baku, Azerbaijan.
AUTHOR
[1] A.N. Barmenkov and A.Y. Kazmin, Completeness of a system of functions of special type. In the book: theory of mappings, some its generalization and applications, Kiev, Naukova Dimka 1982, p.29-43.
1
[2] B.T. Bilalov, On uniform convergence of series in a system of sines, Diff. func., 1988, Vol. 24, No 1, p. 175-177.
2
[3] B.T. Bilalov, Basicity of some systems of functions, Diff. func., 1989, Vol. 25, p. 163-164.
3
[4] B.T. Bilalov, Basicity of some systems of exponents, cosines and sines, Diff. func., 1990, Vol. 26, No 1, p. 10-16.
4
[5] B.T. Bilalov, Basis problems of some systems of exponents, cosines and sines, Sibirskiy matem. zhurnal, 2004, Vol. 45, No 2 , p. 264-273.
5
[6] B.T. Bilalov, On completeness of exponent system with complex coefficients in weight spaces, Trans. of NAS of Azerbaijan, XXV, No 7, 2005, p. 9-14.
6
[7] B.T. Bilalov, On isomorphism of two bases in textbf{$L_{p} $}, Fundam. Prikl. Mat., 1: 4 (1995), 1091-1094.
7
[8] B.T. Bilalov and Z.G. Guseynov, Basicity of a system of exponents with a piece-wise linear phase in variable spaces, Mediterr. J. Math. Vol. 9, No 3 (2012), 487-498.
8
[9] B.T. Bilalov and Z.G. Guseynov, Basicity criterion of perturbed system of exponents in Lebesgue spaces with variable summability index, Dokl. Akad. Nauk, 2011, Vol. 436, No 5, p. 586-589.
9
[10] B.T. Bilalov and A. A. Quliyeva, On basicity of exponential systems in Morrey-type spaces, International Journal of Mathematics. Vol. 25, No. 6 (2014) 1450054 (10 pages).
10
[11] A.V. Bitsadze, On a system of fuctions, UMN, 1950, Vol.5, issue 4 (38), p. 150-151.
11
[12] Y. Chen, Regularity of the solution to the Dirichlet problem in Morrey space, J. Partial Differ. Eqs. 15 (2002) 37-46.
12
[13] G.G. Devdariani, Basicity of a system of sines, Trudy Inst. Prikl. mat. I.N. Vekua, 1987, Vol. 19, p. 21-27.
13
[14] G.G. Devdariani, On basicity of a system of functions, Diff. func., 1986, Vol. 22, No 1, p. 170-171.
14
[15] G.G. Devdariani, On basicity of a system of functions, Diff. func., 1986, Vol. 22, No 1, p. 168-170.
15
[16] G.M. Goluzin, Geometrical theory of a complex variable functions, M., Nauka, 1966, p. 626.
16
[17] D.M. Israfilov and N.P. Tozman, Approximation by polynomials in Morrey-Smirnov classes, East J. Approx. 14(1.3) (2008) 255-269.
17
[18] D.M. Israfilov and N.P. Tozman, Approximation in Morrey-Smirnov classes, Azerbaijan J. Math. 1(1.1) (2011) 99-113.
18
[19] M.I. Kadets, On exact value of Paley-Wiener constant, DAN SSSR, 1964.
19
[20] V. Kokilashvili and A. Meskhi, Boundedness of maximal and singular operators in Morrey spaces with variable exponent, Govern. College Univ. Lahore 72 (2008) 1-11.
20
[21] N.X. Ky, On approximation by trigonometric polynomials in L p u -spaces, Studia Sci. Math. Hungar 28 (1993) 183-188.
21
[22] B. Ya. Levin, Distribution of the roots of entire functions. M., GITL, 1956.
22
[23] A.L. Mazzucato, Decomposition of Besov-Morrey spaces, in "Harmonic Analysis at Mount Holyoke'', American Mathematical Society Contemporary Mathematics, 320 (2003) 279-294.
23
[24] E.I. Moiseev, On basicity of the system of sines and cosines, DAN SSSR, 1984, Vol. 275, No 4, p. 794-798.
24
[25] E.I. Moiseev, On some boundary value problems for mixed equations, Diff. func., 1992, Vol. 28, No 1, p. 123-132.
25
[26] E.I. Moiseev, On the solution of Frankles problem in a special domain, Diff. func., 1992, Vol. 28, No 4, p. 682-692.
26
[27] E.I. Moiseev, On the existence and uniqueness of the solution of a classic problem, Dokl. RAN, 1994, Vol. 336, No 4, p. 448-450.
27
[28] E.I. Moiseev, On basicity of a system of sines, Diff. func., 1987, Vol. 23, No 1, p. 177-179.
28
[29] E.I. Moiseev, On basicity of a system of sines, cosines in weight space. Diff. func., 1998, Vol. 34, No 1, p. 40-44.
29
[30] E.I. Moiseev, On differential properties of expansions in the system of sines and cosines, Diff. func., 1996, Vol. 32, No 1, p.117-126.
30
[31] R. Paley and N. Wiener, Fourier Transforms in the Complex Domain, Amer. Math. Soc. Colloq. Publ., 19 (Amer. Math. Soc., Providence, RI, 1934).
31
[32] J. Peetre, On the theory of spaces, J. Funct. Anal. 4 (1964) 71-87.
32
[33] S.M. Ponomarev, On an eigenvalue problem, DAN SSSR, 1979, Vol. 249, No 5, p. 1068-1070.
33
[34] S.M. Ponomarev, To theory of boundary value problems for mixed type equations in three-dimensional domains, DAN SSSR, 1979, Vol. 246, No 6, p. 1303-1304.
34
[35] S.S. Pukhov and A.M. Sedletskiy, Bases of exponents, sines and cosines in weighs spaces on a finite interval, Dokl. RAN, 2009, Vol. 425, No 4, p. 452-455.
35
[36] D.L. Russel, On exponential bases for the Sobolev spaces over an interval, Journ. of Math. Anal. and Appl., 87, 528-550 (1982).
36
[37] N. Samko, Weight Hardy and singular operators in Morrey spaces, J. Math. Anal. Appl. 35 (1.1) (2009) 183-188.
37
[38] A.M. Sedletskiy, Biorthogonal expansions in series of the exponents on the intervals of a real axis, Usp. Mat. Nauk, 1982, Vol. 37, issue 5 (227), p. 51-95.
38
[39] A.M. Sedletskiy, Approximate properties of a system of exponents in Sobolev spaces, Vestnik Mosc. Univ., ser. 1, math.-mech., 1999, No 6, p. 3-8.
39
[40] C.T. Zorko, Morrey space, Proc. Amer. Math. Soc. 98 (1.4) (1986) 586-592.
40
ORIGINAL_ARTICLE
Results of the Chebyshev type inequality for Pseudo-integral
In this paper, some results of the Chebyshev type integral inequality for the pseudo-integral are proven. The obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. Finally, we applied our results to the case of comonotone functions.
https://scma.maragheh.ac.ir/article_22517_0bef1cf731c3d726fdeb91ce4bbaa098.pdf
2016-11-01
91
100
Additive measure
Chebyshev type inequality
Pseudo-addition
Pseudo-multiplication
Pseudo-integral
Comonotone function
$s$-decomposable fuzzy measure
Bayaz
Daraby
bdaraby@maragheh.ac.ir
1
Department of Mathematics, University of Maragheh, Maragheh, Iran.
LEAD_AUTHOR
[1] J. Caballero and K. Sadaragani, Chebyshev inequality for Sugeno integral, Fuzzy Sets and Systems, 161 (2010) 1480-1487.
1
[2] B. Daraby, Markov type integral inequality for pseudo-integrals, Caspian Journal of Applied Mathematics, Economics and Ecology, Vol. 1, No. 1 (2013) 13-23.
2
[3] B. Daraby and F. Ghadimi, General Minkoski type and related inequalities for seminormed fuzzy integrals, Sahand Communications in Mathematical Analysis, Vol. 1, No. 1 (2014), 9-20.
3
[4] B. Daraby, A. Shafiloo, and A. Rahimi, Generalization of the Feng Qi type inequality for pesudo-integral, Gazi University Journal of Science 28 (4) (2015), 695-702.
4
[5] C. Dellacherie, Quelques commentaires sur les prolongements de capacités, in: Seminaire de Probabilites, (1969/70), Strasbourg, in: Lecture Notes in Mathematics, vol. 191, Springer, Berlin, 1970, pp. 77-81.
5
[6] A. Flores-Franulic, H. Román-Flores, and Y. Chalco-Cano, Markov type inequalities for fuzzy integrals, Appl. Math. Comput. 207 (2009) 242-247.
6
[7] W. Kuich, Semirings, Automata, Languages, Springer-Verlag, Berlin, 1986.
7
[8] R. Mesiar and Y. Ouyang, On the chebyshev type inequality for seminormed fuzzy integral. Appl. Math. lett. 22 (2009) 1810-1815.
8
[9] R. Mesiar and E. Pap, Idempotent integral as limit of g-integrals, Fuzzy Sets and Systems 102 (1999) 385-392.
9
[10] E. Pap, An integral generated by decomposable measure, Univ. Novom Sadu Zb. Rad. Prirod. -Mat. Fak. Ser. Mat. 20 (1) (1990) 135-144.
10
[11] E. Pap, g-calculus, Univ. Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 23 (1) (1993) 145-156.
11
[12] E. Pap, Null-additive Set Functions, Kluwer, Dordrecht, 1995.
12
[13] E. Pap, Generalized real analysis and its applications, Int. J. Approx. Reason. 47 (2008) 368-386.
13
[14] E. Pap and M. Štrboja, Generalization of the Jensen inequality for pseudo-integral, Information Sciences 180 (2010) 543-548.
14
[15] M. Sugeno and T. Murofushi, Pseudo-additive measures and integrals, J. Math. Anal. Appl. 122 (1987) 197-222.
15
ORIGINAL_ARTICLE
On rarely generalized regular fuzzy continuous functions in fuzzy topological spaces
In this paper, we introduce the concept of rarely generalized regular fuzzy continuous functions in the sense of A.P. Sostak's and Ramadan is introduced. Some interesting properties and characterizations of them are investigated. Also, some applications to fuzzy compact spaces are established.
https://scma.maragheh.ac.ir/article_22227_4d3396deccfe38f3630b7cb9f2880ead.pdf
2016-11-01
101
108
Rarely generalized regular fuzzy continuous
Grf-compact space
Rarely grf-almost compact space
Rarely grf-$T_{2}$-spaces
Appachi
Vadivel
avmaths@gmail.com
1
Department of Mathematics, Annamalai University, Annamalainagar, Tamil Nadu-608 002, India.
LEAD_AUTHOR
Elangovan
Elavarasan
maths.aras@gmail.com
2
Research scholar, Department of Mathematics, Annamalai University, Annamalainagar, Tamil Nadu-608 002, India.
AUTHOR
[1] B. Amudhambigai, M.K. Uma, and E. Roja, On rarely $widetilde{g}$-continuous functions in smooth fuzzy topological spaces, The Journal of Fuzzy Mathematics., 20 (2) (2012) 433-442.
1
[2] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968) 182-190.
2
[3] K.C. Chattopadhyay and S.K. Samanta, Fuzzy topology, Fuzzy Sets and Systems, 54 (1993) 207-212.
3
[4] S. Jafari, A note on rarely continuous functions, Univ. Bacau. Stud. Cerc. St. Ser. Mat., 5 29-34.
4
[5] S. Jafari, On some properties of rarely continuous functions, Univ. Bacau. Stud. Cerc. St. Ser. Mat., 7 65-73.
5
[6] S.J. Lee and E.P. Lee, Fuzzy $r$-regular open sets and fuzzy almost $r$-continuous maps, Bull. Korean Math. Soc., 39 (3) (2002) 441-453.
6
[7] N. Levine, Decomposition of continuity in topological spaces, Amer. Math. Monthly., 60 44-46.
7
[8] P.E. Long and L.L. Herrington, Properties of rarely continuous functions, Glasnik Math., 17 (37) 147-153.
8
[9] R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl., 56 (1976) 621-633.
9
[10] V. Popa, Sur certain decompositionde la continuite dans les espaces topologiques, Glasnik Mat. Setr III., 14 (34) 359-362.
10
[11] A.A. Ramadan, S.E. Abbas, and Y.C. Kim, Fuzzy irresolute mappings in smooth fuzzy topological spaces, The Journal of Fuzzy Mathematics., 9 (2001) 865-877.
11
[12] P. Smets, The degree of belief in a fuzzy event, Inform. Sci., 25 (1981) 1-19.
12
[13] M. Sugeno, An introductory survey of fuzzy control, Inform. Sci., 36 (1985) 59-83.
13
[14] A.P. Šostak, On a fuzzy topological structure, Rend. Circ. Matem. Palermo Ser II., 11 (1986) 89-103.
14
[15] A.P. Šostak, On the neighborhood structure of a fuzzy topological spaces, Zh. Rodova Univ. Nis. Ser. Math., 4 (1990) 7-14.
15
[16] A.P. Šostak, Basic structures of fuzzy topology, J. Math. Sci., 78 (6) (1996) 662-701.
16
[17] A. Vadivel and E. Elavarasan, Applications of $r$-generalized regular fuzzy closed sets, Annals of Fuzzy Mathematics and Informatics (Accepted).
17
[18] L.A. Zadeh, Fuzzy sets, Information and control., 8 (1965) 338-353.
18