Abstract
Abstract In this paper, we construct a new family of operators, prove some approximation results in A-statistical sense and establish some direct theorems for Kantorovich-type integral operators. MSC: Primary 41A10, 41A25, 41A36.
Highlights
1 Introduction and preliminaries Statistical convergence [ ] and its variants, extensions and generalizations have been proved to be an active area of recent research in summability theory, e.g., lacunary statistical convergence [ ], λ-statistical convergence [ ], A-statistical convergence [ ], statistical A-summability [ ], statistical summability (C, ) [ ], statistical summability (H, ) [ ], statistical summability (N, p) [ ] and statistical σ -summability [ ] etc
Following the work of Gadjiv and Orhan [ ], these statistical summability methods have been used in establishing many approximation theorems (e.g., [, – ] and [ ])
We construct a new family of operators with the help of Erkuş-Srivastava polynomials, establish some A-statistical approximation properties and direct theorems
Summary
Un(α, ,.,....,.α, rr)(x , . . . , xr), which are defined by the following generating function [ , p. , Eq ( )]:. Xr), which are defined by the following generating function [ , p. |xr|– / r , are a unification (and generalization) of several known families of multivariable polynomials including (for example) Chan-Chyan-Srivastava polynomials gn(α ,...,αr)(x , . The Chan-Chyan-Srivastava polynomials gn(α ,...,αr)(x , . Xr) follow as a special case of the polynomials due to Erkuş and Srivastava [ ]. Xr) follow as a special case of the polynomials [ ] Un(α, ,.,....,.α, rr)(x , . ). The following relationship is established between the polynomials due to Erkuş and Srivastava [ ] and the Chan-Chyan-Srivastava polynomials by applying the generating functions By using the Erkuş-Srivastava multivariable polynomials given by = Tnω( , ),ω( , ) (f ; x) – xTnω( , ),ω( , ) (f ; x) + x , it follows from Lemma .
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