A note on Baskakov operators based on a function ϑ

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.