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http://dx.doi.org/10.5666/KMJ.2016.56.3.877

Szász-Kantorovich Type Operators Based on Charlier Polynomials  

Kajla, Arun (Department of Mathematics, Indian Institute of Technology Roorkee)
Agrawal, Purshottam Narain (Department of Mathematics, Indian Institute of Technology Roorkee)
Publication Information
Kyungpook Mathematical Journal / v.56, no.3, 2016 , pp. 877-897 More about this Journal
Abstract
In the present article, we study some approximation properties of the Kantorovich type generalization of $Sz{\acute{a}}sz$ type operators involving Charlier polynomials introduced by S. Varma and F. Taşdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). First, we establish approximation in a Lipschitz type space, weighted approximation theorems and A-statistical convergence properties for these operators. Then, we obtain the rate of approximation of functions having derivatives of bounded variation.
Keywords
Kantorovich operator; Charlier polynomials; modulus of continuity; A-statistical convergence; bounded variation;
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1 T. Acar, V. Gupta and A. Aral, Rate of convergence for generalized Szasz operators, Bull. Math. Sci. 1(1)(2011), 99-113.   DOI
2 P. N. Agrawal, Z. Finta and A. S. Kumar, Bernstein-Schurer-Kantorovich operators based on q-integers, Appl. Math. Comput. 256(2015), 222-231.
3 P. N. Agrawal, V. Gupta, A. S. Kumar and A. Kajla, Generalized Baskakov-Szasz type operators, Appl. Math. Comput. 236(2014), 311-324.
4 F. Altomare, M. C. Montano and V. Leonessa, On a generalization of Szasz-Mirakjan- Kantorovich operators, Results Math. 63(2013), 837-863.   DOI
5 G. A. Anastassiou and O. Duman, A Baskakov type generalization of statistical Korovkin theory, J. Math. Anal. Appl. 340(2008), 476-486.   DOI
6 G. Bascanbaz-Tunca and A. Erencin, A Voronovskaya type theorem for q-Szasz- Mirakyan-Kantorovich operators, Revue d'Analyse Numerique et de Theorie de l'Approximation, 40(1)(2011), 14-23.
7 P. L. Butzer, On the extensions of Bernstein polynomials to the in nite interval, Proceedings of the American Mathematical Society, 5(1954), 547-55.   DOI
8 T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, NewYork, (1978).
9 R. A. Devore and G. G. Lorentz, Constructive Approximation, Springer, Berlin (1993).
10 E. E. Duman and O. Duman, Statistical approximation properties of high order opera- tors constructed with the Chan-Chayan-Srivastava polynomials, Appl. Math. Comput. 218(2011), 1927-1933.
11 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.
12 O. Duman and C. Orhan, Statistical approximation by positive linear operators, Studia Math. 161(2)(2004), 187-197.   DOI
13 V. Gupta and R. P. Agarwal, Convergence Estimates in Approximation Theory, Springer, (2014).
14 O. Duman, M. A. O zarslan and B. Della Vecchia, Modi ed Szasz-Mirakjan- Kantorovich operators preserving linear functions, Turkish Journal of Mathematics, 33(2)(2009), 151-158.
15 A. D. Gadjiev, R. O. Efendiyev and E. Ibikli, On Korovkin type theorem in the space of locally integrable functions, Czech. Math. J. 53(128)(2003), 45-53.   DOI
16 A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain. J. Math. 32(1)(2002), 129-138.   DOI
17 E. Ibikli and E. A. Gadjieva, The order of approximation of some unbounded function by the sequences of positive linear operators, Turkish J. Math. 19(3)(1995), 331-337.
18 M. E. H. Ismail, Classical and Quantum Orthogonal Polynomials in One Variable, Cambridge University Press, Cambridge (2005).
19 N. Ispir, Rate of convergence of generalized rational type Baskakov operators, Math. Comput. Modelling. 46(5-6)(2007), 625-631.   DOI
20 N. Ispir and V. Gupta, A- statistical approximation by the generalized Kantorovich- Bernstein type rational operators, Southeast Asian Bull. Math. 32(2008), 87-97.
21 A. Jakimovski and D. Leviatan, Generalized Szasz operators for the approximation in the in nite interval, Mathematica (Cluj) 34(1969), 97-103.
22 A. Kajla and P. N. Agrawal, Szasz-Durrmeyer type operators based on Charlier polynomials, Appl. Math. Comput. 268(2015), 1001-1014.
23 H. Karsli, Rate of convergence of new gamma type operators for functions with deriva- tives of bounded variation, Math. Comput. Modelling. 45(5-6)(2007), 617-624.   DOI
24 D. Miclaus, The Voronovskaja type theorem for the Szasz-Mirakjan-Kantorovich operators, Journal of Science and Arts, 2(13)(2010), 257-260.
25 M. A. Ozarslan, O. Duman and C. Kaanoglu, Rates of convergence of certain King- type operators for functions with derivative of bounded variation, Math. Comput. Modelling. 52(1-2)(2010), 334-345.   DOI
26 G. Nowak and A. Sikorska-Nowak, Some approximation properties of modi ed Szasz- Mirakyan-Kantorovich operators, Revue d'Analyse Numerique et de Theorie de l'Approximation, 38(1)(2009), 73-82.
27 M. Orkcu and O. Dogru, Statistical approximation of a kind of Kantorovich type q-Szasz-Mirakjan operators, Nonlinear Anal. 75(2012), 2874-2882.   DOI
28 M. Orkcu and O. Dogru, Weighted statistical approximation by Kantorovich type q- Szasz-Mirakjan operators. Appl. Math. Comput. 217(20)(2011), 7913-7919.   DOI
29 M. A. Ozarslan and H. Aktuglu, Local approximation for certain King type operators, Filomat 27(1), 173{181.   DOI
30 C. Radu, On statistical approximation of a general class of positive linear operators extended in q-calculus, Appl. Math. Comput. 215(2009), 2317-2325.
31 O. Szasz, Generalization of S. Bernsteins polynomials to the in nite interval, J. Res. Nat. Bur. Standards 45(1950), 239-245.   DOI
32 V. Totik, Approximation by Szasz-Mirakjan-Kantorovich operators in $L^p$(p > 1), Analysis Mathematica, 9(2)(1983), 147-167.   DOI
33 S. Varma, S. Sucu and G. Icoz, Generalization of Szasz operators involving Brenke type polynomials, Comput. Math. Appl. 64(2012), 121-127.   DOI
34 S. Varma and F. Tasdelen, Szasz type operators involving Charlier polynomials, Math. Comput. Modelling, 56(2012), 118{122.   DOI
35 Z.Walczak, On approximation by modi ed Szasz-Mirakyan operators, Glasnik Matematicki, 37(57)(2002), 303{319.
36 I. Yuksel and N. Ispir, Weighted approximation by a certain family of summationintegral-type operators, Comput. Math. Appl. 52(10-11)(2006), 1463-1470.   DOI