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.

Jain's operator: A new construction and applications in approximation theory

“…In addition to these, Cárdenas‐Morales et al [23] showed that a new class of Bernstein‐type operators, which defined based on , preserves instead of classical Korovkin test functions, . With this motivation, different types of generalizations have been presented for another type of positive linear operators such as Bersntein–Durmeyyer‐type operators in Acar et al [24], Szász–Mirakyan‐type operators in Aral et al [25], Bernstein–Chlodowsky‐type operators in Usta [26], Balázs‐type operators in Usta [27], Baskakov‐type operators in Usta [28], Meyer–König and Zeller‐type operators in Cai et al [29], and Gamma‐type operators in Erençin and Raşa [30].…”