Some results on generalized Szász operators involving Sheffer polynomials
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摘要
In this paper we consider old and new operators of Szász type involving Sheffer polynomials. We present an asymptotic expansion formula for operators of Ismail type. Then, in order to improve the accuracy of the approximation of a function f in a fixed point, we apply a well-known extrapolation algorithm. We also introduce some new special sequences of Appell and Sheffer polynomials and construct new generalized Szász-type operators. By using classical techniques we investigate approximation properties and rate of convergence for these operators and compare the results with other existing operators. Finally, we present numerical examples which confirm the validity of the theoretical analysis and the effectiveness of the presented operators.
论文关键词:41A36,41A25,33E99,Szász operator,Sheffer polynomials,Asymptotic expansion,Rate of convergence,Extrapolation
论文评审过程:Received 11 October 2017, Revised 17 January 2018, Available online 5 February 2018, Version of Record 5 February 2018.
论文官网地址:https://doi.org/10.1016/j.cam.2018.01.016