Some convergence results for nonlinear Baskakov-Durrmeyer operators

Authors

https://doi.org/10.15330/cmp.15.1.95-103

Keywords:

bounded variation, nonlinear operator, (Lψ)(Lψ) Lipschitz condition, pointwise convergence
Published online: 2023-06-18

Abstract

This paper is an introduction to a sequence of nonlinear Baskakov-Durrmeyer operators (NBDn)(NBDn) of the form (NBDn)(f;x)=0Kn(x,t,f(t))dt(NBDn)(f;x)=0Kn(x,t,f(t))dt with x[0,)x[0,) and nN. While Kn(x,t,u) provide convenient assumptions, these operators work on bounded functions, which are defined on all finite subintervals of [0,). This paper comprise some pointwise convergence results for these operators in certain functional spaces. As well as this study can be seen as a continuation of studies about nonlinear operators, it is the first study on nonlinear Baskakov-Durrmeyer or modified Baskakov operators, while there were more papers on linear part of the operators.

How to Cite
(1)
Altin, H. Some Convergence Results for Nonlinear Baskakov-Durrmeyer Operators. Carpathian Math. Publ. 2023, 15, 95-103.