Approximation by complex Stancu Beta operators of second kind in semidisks

Sorin G. Gal; Vijay Gupta

doi:10.33993/jnaat421-980

Authors

Sorin G. Gal University of Oradea, Romania
Vijay Gupta Netaji Subhas Institute of Technology, India

DOI:

https://doi.org/10.33993/jnaat421-980

Keywords:

complex Stancu Beta operator of second kind, semidisk of the right half-plane, simultaneous approximation, Voronovskaja-type result, exact degrees of approximation

Abstract views: 237

Abstract

In this paper, the exact order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for the complex Stancu Beta operator of second kind attached to analytic functions of exponential growth in semidisks of the right half-plane are obtained. In this way, we show the overconvergence phenomenon for this operator, namely the extensions of approximation properties with upper and exact quantitative estimates, from the real subinterval \((0, r]\), to semidisks of the right half-plane of the form \(SD^{r}(0, r]=\{z\in \mathbb{C}: |z|\le r, \, 0 < {\rm Re}(z)\le r\}\) and to subsets of semidisks of the form \(SD^{r}[a, r]=\{z\in \mathbb{C}: |z|\le r, \, a\le {\rm Re}(z)\le r\}\), with \(r\ge 1\) and \(0<a<r\).

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