Jakimovski–Leviatan operators of Durrmeyer type involving Appell polynomials

Jakimovski–Leviatan operators of Durrmeyer type involving Appell polynomials

The purpose of the present paper is to establish the rate of convergence for a Lipschitz-type space andobtain the degree of approximation in terms of Lipschitz-type maximal function for the Durrmeyer type modification ofJakimovski–Leviatan operators based on Appell polynomials. We also study the rate of approximation of these operatorsin a weighted space of polynomial growth and for functions having a derivative of bounded variation.

___

  • [1] Acar T, Gupta V, Aral A. Rate of convergence for generalized Sz´asz operators. Bull Math Sci 2011; 1: 99-113.
  • [2] Agrawal PN, Gupta V, Kumar AS, Kajla A. Generalized Baskakov-Sz´asz type operators, Appl Math Comput 2014; 236: 311-324.
  • [3] Aral A, Acar T. Weighted approximation by new Bernstein-Chlodowsky-Gadjiev operators. Filomat 2013; 27: 371- 380.
  • [4] Gadjiev AD, Efendiyev RO, ˙Ibikli E. On Korovkin type theorem in the space of locally integrable functions. Czechoslovak Math J 2003; 53: 45-53.
  • [5] Goyal M, Gupta V, Agrawal PN. Quantitative convergence results for a family of hybrid operators. Appl Math Comput 2015; 271: 893-904.
  • [6] Gupta V, Greubel GC. Moment estimations of new Sz´asz-Mirakyan-Durrmeyer operators. Appl Math Comput 2015; 271: 540-547.
  • [7] İbikli E, Gadjieva EA. The order of approximation of some unbounded functions by the sequences of positive linear operators. Turk J Math 1995; 19: 331-337.
  • [8] Jakimovski A, Leviatan D. Generalized Sz´asz operators for the approximation in the infinite interval. Mathematica 1969; 34: 97-103.
  • [9] Kajla A, Agrawal PN. Sz´asz-Durrmeyer type operators based on Charlier polynomials. Appl Math Comput 2015; 268: 1001-1014.
  • [10] Karaisa A. Approximation by Durrmeyer type Jakimovski-Leviatan operators. Math Method Appl Sci 2016; 39: 2401-2410.
  • [11] Karsli H. Rate of convergence of new Gamma type operators for functions with derivatives of bounded variation. Math Comput Modelling 2007; 45: 617-624.
  • [12] Karsli H. Rate of convergence of Cholodowsky operators for functions with derivatives of bounded variation. Appl Math E-Notes 2008; 8: 203-213.
  • [13] Karsli H, Agrawal PN, Goyal M. General Gamma type operators based on q -integers. Appl Math Comput 2015; 251: 564-575.
  • [14] Lenze B. On Lipschitz-type maximal functions and their smoothness spaces. Nederl Akad Wetensch Indag Math 1988; 50: 53-63.
  • [15] Ozarslan MA, Duman O. Local approximation behaviour of modified SMK operators. Miskolc Math Notes 2010; ¨ 11: 87-99.
  • [16] Ozarslan MA, Duman O, Kaano˘glu C. Rate of convergence of certain King-type operators for functions with ¨ derivatives of bounded variation. Math Comput Modelling 2010; 52: 334-345.
  • [17] Yüksel I, Ispir N. Weighted approximation by a certain family of summation integral-type operators. Comput Math Appl 2006; 52: 1463-1470.