The generalization of the ?-Meyer-König-Zeller operators by generating functions

Abstract

In this paper, we introduce generating functions type alpha-Meyer-K & ouml;nig and Zeller operators. We prove a new Korovkin type theorem by using appropriate auxiliary test functions. Also, we obtain functional partial differential equation which help us to calculate the moments easily. Secondly, we compute the rate of approximation by means of the Lipchitz class functionals. Moreover, we introduce the particular form of the operators namely the alpha-type Alkemade's Meyer K & ouml;nig and Zeller operators, and study their approximation properties. Also, Graphical and numerical examples are provided to illustrate the effectiveness of approximation using these operators. Finally, a real-world health case study involving monkeypox cases in the Democratic Republic of the Congo is explored to showcase the modeling capabilities of these operators.