A Note on Uniformly Convergence for Positive Linear Operators Involving Euler Type Polynomials

Year 2024, Volume: 1 Issue: 1, 13 - 18, 27.05.2024

Erkan Ağyüz

Abstract

Positive linear operators play a significant role in many domains, particularly numerical and mathematical analysis. Specifically, they are commonly found in a wide variety of methods to resolve optimization and differential equation issues. Basic properties of positive linear operators are linearity, positivity, positive linear and being restrictive. There are various ways to examine the significance of positive linear operators in Approximation Theory. The Convergence Analysis is the most significant of these. In many situations involving numerical analysis and convergence analysis, positive linear operators are essential. Positive linear operators must be able to converge in iterations towards a specific goal, especially in various approximation techniques or iterative solution algorithms. This can be used to solve optimization issues more effectively or to increase the precision of numerical answers. In approximation theory, generating functions are essential. They are specifically used to build algorithms that facilitate the proper approximation to a goal and to examine the approximation in question. The speed at which an approximation converges to a target can also be ascertained via generating functions. An essential tool for evaluating and enhancing the rate of convergence of iterative algorithms is offered by these functions. The aim of this study is to construct a generalized Kantorovich type Szász operators including the generating functions of Euler polynomials with order (-1). Moreover, we derive the moment and central moment functions for these operators. Finally, we show uniformly convergence of operators by using Korovkin theorem.

Keywords

Positive linear operators, Generating functions, Euler type polynomials, Korovkin Theorem, Moment functions

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