Approximation by a kind of complex modified q-Durrmeyer type operators in compact disksReport as inadecuate




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Journal of Inequalities and Applications

, 2012:212

First Online: 02 October 2012Received: 25 March 2012Accepted: 07 September 2012

Abstract

In this paper, in order to make the convergence faster to a function being approximated, we introduce a kind of complex modified q-Durrmeyer type operators which can reproduce constant and linear functions. We study the approximation properties of these operators. We obtain the order of simultaneous approximation and a Voronovskaja-type result with a quantitative estimate for these complex modified q-Durrmeyer type operators attached to analytic functions on compact disks. More important, our results show the overconvergence phenomenon for these complex operators.

MSC: 30E10, 41A25.

Keywordscomplex modified q-Durrmeyer type operators simultaneous approximation Voronovskaja-type result overconvergence q-calculus  Download fulltext PDF



Author: Mei-Ying Ren - Xiao-Ming Zeng

Source: https://link.springer.com/




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