A Note on New Construction of Meyer-König and Zeller Operators and Its Approximation Properties

Abstract

The topic of approximation with positive linear operators in contemporary functional analysis and theory of functions has emerged in the last century. One of these operators is Meyer–König and Zeller operators and in this study a generalization of Meyer–König and Zeller type operators based on a function τ by using two sequences of functions will be presented. The most significant point is that the newly introduced operator preserves {1,τ,τ2} instead of classical Korovkin test functions. Then asymptotic type formula, quantitative results, and local approximation properties of the introduced operators are given. Finally a numerical example performed by MATLAB is given to visualize the provided theoretical results.

Keywords

• Meyer–König and Zeller operators
• modulus of continuity
• shape preserving approximation
• Voronovskaya theorem
• Korovkin type theorem