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http://dx.doi.org/10.5666/KMJ.2019.59.4.679

Statistical Approximation of Szász Type Operators Based on Charlier Polynomials  

Kajla, Arun (Department of Mathematics, Central University of Haryana)
Publication Information
Kyungpook Mathematical Journal / v.59, no.4, 2019 , pp. 679-688 More about this Journal
Abstract
In the present note, we study some approximation properties of the Szász type operators based on Charlier polynomials introduced by S. Varma and F. Taşdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). We establish the rates of A-statistical convergence of these operators. Finally, we prove a Voronovskaja type approximation theorem and local approximation theorem via the concept of A-statistical convergence.
Keywords
$Sz{\acute{a}}sz$ operator; Charlier polynomials; modulus of continuity; statistical convergence; bounded variation;
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1 R. A. Devore and G. G. Lorentz, Constructive approximation, Springer-Verlag, Berlin, 1993.
2 E. E. Duman and O. Duman, Statistical approximation properties of high order operators constructed with the Chan-Chayan-Srivastava polynomials, Appl. Math. Comput., 218(2011), 1927-1933.   DOI
3 E. E. Duman, O. Duman and H. M. Srivastava, Statistical approximation of certain positive linear operators constructed by means of the Chan-Chayan-Srivastava polynomials, Appl. Math. Comput., 182(2006), 231-222.
4 O. Duman and C. Orhan, Statistical approximation by positive linear operators, Studia Math., 161(2)(2004), 187-197.   DOI
5 Z. Finta, N. K. Govil and V. Gupta, Some results on modified Szasz-Mirakjan operators, J. Math. Anal. Appl., 327(2007), 1284-1296.   DOI
6 A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain. J. Math., 32(1)(2002), 129-138.   DOI
7 V. Gupta and R. P. Agarwal, Convergence estimates in approximation theory, Springer, Cham, 2014.
8 A. Ciupa, On a generalized Favard-Szasz type operator, Research Seminar on Numerical and Statistical Calculus,, 33-38, Preprint 94-1, Babes-Bolyai Univ. Cluj-Napoca, 1994.
9 V. Gupta and M. A. Noor, Convergence of derivatives for certain mixed Szasz-Beta operators, J. Math. Anal. Appl., 321(2006), 1-9.   DOI
10 V. Gupta, T. M. Rassias, P. N. Agrawal and A. M. Acu, Recent advances in constructive approximation theory, Springer Optimization and Its Applications 138. Springer, Cham, 2018.
11 V. Gupta and G. Tachev, Approximation with positive Linear operators and linear combinations, Developments in Mathematics 50, Springer, Cham, 2017.
12 A. Kajla and P. N. Agrawal, Szasz-Kantorovich type operators based on Charlier polynomials, Kyungpook Math. J., 56(2016), 877-897.   DOI
13 V. Gupta, G. Tachev, and A. M. Acu, Modified Kantorovich operators with better approximation properties, Numer. Algorithms, 81(2019), 125--149.   DOI
14 M. E. H. Ismail, Classical and quantum orthogonal polynomials in one variable, Encyclopedia of Mathematics and its Applications 98. Cambridge University Press, Cambridge, 2009.
15 A. Jakimovski and D. Leviatan, Generalized Szasz operators for the approximation in the infinite interval, Mathematica (Cluj), 34(1969), 97-103.
16 A. Kajla and P. N. Agrawal, Approximation properties of Szasz type operators based on Charlier polynomials, Turkish. J. Math., 39(2015), 990-1003.   DOI
17 M. Orkcu and O. Dogru, Statistical approximation of a kind of Kantorovich type q-Szasz-Mirakjan operators, Nonlinear Anal., (75)(2012), 2874-2882.
18 H. S. Kasana, G. Prasad, P. N. Agrawal and A. Sahai, Modified Szasz operators, Mathematical analysis and its applications (Kuwait, 1985), 29-41, KFAS Proc. Ser. 3, Pergamon, Oxford, 1988.
19 S. M. Mazhar and V. Totik, Approximation by modified Szasz operators, Acta Sci. Math., 49(1985), 257-269.
20 M. Orkcu and O. Dogru, Weighted statistical approximation by Kantorovich type q-Szasz-Mirakjan operators. Appl. Math. Comput., 217(20)(2011), 7913-7919.   DOI
21 M. A. Ozarslan, A-statistical converegence of Mittag-Leffler operators, Miskolc Math. Notes, 14(2013), 209-217.   DOI
22 C. Radu, On statistical approximation of a general class of positive linear operators extended in q-calculus, Appl. Math. Comput., 215(2009), 2317-2325.   DOI
23 C . Atakut and N. Ispir, Approximation by modified Szasz-Mirakjan operators on weighted spaces, Proc. Indian Acad. Sci. Math. Sci., 112(2002), 571-578.   DOI
24 O. Szasz, Generalization of S. Bernstein's polynomials to the infinite interval, J. Res. Nat. Bur. Standards, 45(1950), 239-245.   DOI
25 S. Varma, S. Sucu and G. Icoz, Generalization of Szasz operators involving Brenke type polynomials, Comput. Math. Appl., 64(2012), 121-127.   DOI
26 S. Varma and F. Tasdelen, Szasz type operators involving Charlier polynomials, Math. Comput. Modelling, 56(2012), 118-122.   DOI
27 F. Altomare, M. C. Montano and V. Leonessa, On a generalization of Szasz-Mirakjan-Kantorovich operators, Results Math., 63(2013), 837-863.   DOI
28 G. A. Anastassiou and O. Duman, A Baskakov type generalization of statistical Korovkin theory, J. Math. Anal. Appl., 340(2008), 476-486.   DOI
29 A. Aral, A generalization of Szasz-Mirakyan operators based on q-integers, Math. Comput. Modelling, 47(9/10)(2008), 1052-1062.   DOI
30 A. Aral and O. Duman, A Voronovskaya type forumla for SMK operators via statistical convergence, Math. Slovaca, 61(2011), 235-244.   DOI