Approximation by Bernstein-Kantorovich type operators based on beta function

Abstract

With the idea taken from the King type operators which preserve some test functions, we introduce here some Durrmeyer variants of Bernstein operators based on Beta functions. Some direct approximation theorems are provided of this introduced sequence of operators. We also proved Voronovkaja type theorem. Furthermore, graphical and numerical examples are also given with the help of MATLAB.