Convergence analysis of modified Bernstein–Kantorovich type operators

Abstract

In the present paper, we introduce a new Kantorovich variant of modified Bernstein Operators. First, we discuss some auxiliary results and present a Korovkin-type theorem for the newly defined operators. Next, we examine the rate of convergence of the operators with the help of the modulus of continuity and Peetre’s K-functionals. Also, we discuss a global approximation result with the help of the Ditzian-Totik uniform modulus of smoothness and propose a convergence result for a Lipschitz class of functions. Furthermore, we present a quantitative Voronovskaja type asymptotic result as well as a Grüss-Voronovskaja type result for the new operators. Lastly, we validate our theoretical results with the help of some graphs using Mathematica software. © 2023, The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature.