Placeholder

A note on Baskakov operators based on a function ϑ


DIDEM AYDIN ARI, ALI ARAL, DANIEL CARDENAS ´ -MORALES


Full PDF

abs_cmi_2016_25_15-27v1

In this paper, we consider a modification of the classical Baskakov operators based on a function ϑ. Basic qualitative and quantitative Korovkin
results 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.