Approximation on Durrmeyer modification of generalized Szasz-Mirakjan operators

TL;DR

This paper investigates the approximation properties of Durrmeyer-type generalizations of Szasz-Mirakjan operators, providing theoretical results, convergence analysis, and numerical illustrations.

Contribution

It introduces a Durrmeyer modification of Szasz-Mirakjan operators and establishes new approximation theorems and convergence results.

Findings

Established direct approximation results.

Proved a quantitative Voronovskaya type theorem.

Provided numerical and graphical comparisons.

Abstract

This paper deals with the approximations of Durrmeyer type generalization of Szasz-Mirakjan operators. We establish the direct results, quantitative Voronovskaya type theorem, Gruss type theorem, A-statistical convergence, rate of convergence in terms of the function with derivative of bounded variation. At last, the graphical analysis, comparison study and numerical representations of proposed operators are discussed.