Higher Order Approximation of Continuous Functions by a Modified Meyer-König and Zeller-Type Operator

2025/06/17 by Ivan Gadjev, Gadjev, Ivan, П. Парванов +3
Mathematics · #41A10 #41A17 #41A25 #41A27 #41A35 #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fixed Point Theorems Analysis #Iterative Methods for Nonlinear Equations

paper · pdf · doi:10.48550/arxiv.2506.14392

openalex publication_date 2025/06/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

A new Goodman-Sharma type modification of the Meyer-König and Zeller operator for approximation of bounded continuous functions on [0,1) is presented. We estimate the approximation error of the proposed operator and prove direct and strong converse theorems with respect to a related K-functional. The operator is linear but not a positive one. However it benefits a better order of approximation compared to the Goodman-Sharma variant of Meyer-König and Zeller type operator investigated by Ivanov and Parvanov in 2012.

Citations

• On a New Modification of Baskakov Operators with Higher Order of Approximation
• Higher Order Approximation of Functions by Modified Goodman-Sharma Operators
• Better approximation of functions by genuine Bernstein-Durrmeyer type operators

Related

• Higher Order Approximation of Functions by Modified Goodman-Sharma Operators
• On a New Modification of Baskakov Operators with Higher Order of Approximation
• On Better Approximation Order for the Max-Product Meyer-König and Zeller Operator
• Approximation by Meyer-Konig and Zeller Operators using (p, q)-CALCULUS
• Approximation properties of (p,q)-Meyer-Konig-Zeller Durrmeyer operators