Korovkin Type Theorem for the functions deÖned in the Prism and the corresponding Meyer-Kˆnig and Zeller operators

Abstract

In this paper, we consider Meyer-König and Zeller (MKZ) operators deÖned in the prism. We prove a new Korovkin type theorem by using appropriate auxiliary test function and investigate the uniform approximation of these operators. We obtain the order of approximation in terms of the modulus of continuity and modiÖed Lipschitz functions. Finally, we introduce the more general form of the operators and study their approximation properties by obtaining functional partial di§erential equation which help us to calculate the moments easily.