Some approximation results for the new modification of Bernstein-Beta operators

Abstract

This paper deals with the newly modification of Beta-type Bernstein operators, preserving constant and Korovkin's other test functions $ e_i = t^i $, $ i = 1, 2 $ in limit case. Then the uniform convergence of the constructed operators is given. The rate of convergence is obtained in terms of modulus of continuity, Peetre-$ \mathcal{K} $ functionals and Lipschitz class functions. After that, the Voronovskaya-type asymptotic result for these operators is established. At last, the graphical results of the newly defined operators are discussed.

Keywords

• korovkin type approximation theorem
• modulus of continuity
• functions of lipschitz class
• peetre's k-functionals