Approximation by complex summation-integral type operator in compact disks

Mathematica Slovaca

Rani Yadav¹  Vijay Gupta¹ 

关键词: complex Durrmeyer-type operators;    uniform convergence;    analytic function;    Voronovskaja-type result;   

DOI  :  10.2478/s12175-013-0152-z

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

In the present paper we estimate a Voronovskaja type quantitative estimate for a certain type of complex Durrmeyer polynomials, which is different from those studied previously in the literature. Such estimation is in terms of analytic functions in the compact disks. In this way, we present the evidence of overconvergence phenomenon for this type of Durrmeyer polynomials, namely the extensions of approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane. In the end, we mention certain applications.

【 授权许可】

Unknown