A note on Baskakov operators based on a function ϑ


Ari, Didem Aydin, Aral, Ali and Cárdenas-Morales, Daniel


Abstract

creative_2016_25_1_015_027_abstract

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creative_2016_25_1_015_027

In this paper, we consider a modification of the classical Baskakov operators based on a function ϑ. Basic qualitative and quantitative Korovk inresults are stated in weighted spaces. We prove a quantitative Voronovskaya-type theorem and present some results on the monotonic convergence of the sequence. Finally, we show a shape preserving property and further direct convergence theorems. Weighted modulus of continuity of first order and the notion of ϑ-convexity are used throughout the paper.

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Author(s)

Aral, Ali, Ari, Didem Aydin, Cárdenas-Morales, Daniel