Approximation properties of Sz´asz type operators based on Charlier polynomials

Approximation properties of Sz´asz type operators based on Charlier polynomials

: In the present paper, we study some approximation properties of the Sz´asz type operators involving Charlier polynomials introduced by Varma and Ta¸sdelen in 2012. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain the error in the approximation of functions having derivatives of bounded variation.

___

  • Acar T, Gupta V, Aral A. Rate of convergence for generalized Sz´asz operators. Bull Math Sci 2011; 1: 99–113.
  • Agrawal PN, Gupta V, Kumar AS, Kajla A. Generalized Baskakov-Sz´asz type operators. Appl Math Comput 2014; 236: 311–324.
  • Altomare F, Montano MC, Leonessa V. On a generalization of Sz´asz-Mirakjan-Kantorovich operators. Results Math 2013; 63: 837–863.
  • Aral A. A generalization of Sz´asz-Mirakyan operators based on q-integers. Math Comput Modelling 2008; 47: 1052–1062.
  • Atakut C¸, Ispir N. Approximation by modified Sz´asz-Mirakjan operators on weighted spaces. Proc Indian Acad Sci Math 2002; 112: 571–578.
  • C´ardenas-Morales D, Gupta V. Two families of Bernstein-Durrmeyer type operators. Appl Math Comput 2014; 248: 342–353.
  • Ciupa A. On a generalized Favard-Sz´asz type operator. Research Seminar on Numerical and Statistical Calculus, Univ. Babe¸s Bolyai Cluj-Napoca, Preprint 1994; 1: 33–38.
  • Finta Z, Govil NK, Gupta V. Some results on modified Sz´asz-Mirakjan operators. J Math Anal Appl 2007; 327: 1284–1296.
  • Gadjiev AD. On P. P. Korovkin type theorems. Math Zametki 1976; 20: 781–786.
  • Gadjiev AD, Efendiyev RO, Ibikli E. On Korovkin type theorem in the space of locally integrable functions. Czech Math J 2003; 53: 45–53.
  • Ismail MEH. Classical and Quantum Orthogonal Polynomials in One Variable. Cambridge, UK: Cambridge University Press, 2005.
  • Ispir N. Rate of convergence of generalized rational type Baskakov operators. Math Comput Modelling 2007; 46: 625–631.
  • Jakimovski A, Leviatan D. Generalized Sz´asz operators for the approximation in the infinite interval. Mathematica (Cluj) 1969; 34: 97–103.
  • Karsli H. Rate of convergence of new gamma type operators for functions with derivatives of bounded variation. Math Comput Modelling 2007; 45: 617–624.
  • Kasana HS, Prasad G, Agrawal PN, Sahai A. Modified Sz´asz operators. In: Proceedings of the Conference on Mathematical Analysis and Its Applications, Kuwait. Oxford, UK: Pergamon Press, 1985, 29–42.
  • Lenze B. On Lipschitz type maximal functions and their smoothness spaces. Nederl Akad Indag Math 1988; 50: 53–63.
  • Mazhar SM, Totik V. Approximation by modified Sz´asz operators. Acta Sci Math 1985; 49: 257–269.
  • Ozarslan MA, Aktuˇglu H. Local approximation for certain King type operators. Filomat 2013; 27: 173–181. ¨
  • Ozarslan MA, Duman O, Kaano ˇ ¨ g lu C. Rates of convergence of certain King-type operators for functions with derivative of bounded variation. Math Comput Modelling 2010; 52: 334–345.
  • Sz´asz O. Generalization of S. Bernstein’s polynomials to the infinite interval. J Res Nat Bur Standards 1950; 45: 239–245.
  • Varma S, Sucu S, I¸c¨oz G. Generalization of Sz´asz operators involving Brenke type polynomials. Comput Math Appl 2012; 64: 121–127.
  • Varma S, Ta¸sdelen F. Sz´asz type operators involving Charlier polynomials. Math Comput Modelling 2012; 56: 118–122.