Approximation by a generalization of the Jakimovski -Leviatan operators

TL;DR

This paper introduces a Kantorovich generalization of Jakimovski-Leviatan operators, establishing convergence theorems and analyzing their behavior in weighted function spaces on the positive semi-axis.

Contribution

The paper presents a new Kantorovich-type generalization of Jakimovski-Leviatan operators with proven convergence properties and analysis in weighted spaces.

Findings

Operators converge in weighted spaces

Theorems on degree of convergence established

Extension of classical operators to new generalized form

Abstract

In this paper, we introduce a Kantorovich type generalization of Jakimovski-Leviatan operators constructed by A. Jakimovski and D. Leviatan (1969) and the theorems on convergence and the degrree of convergence are established. Furthermore, we study the convergence of these operators in a weighted space of functions on a positive semi-axis.