On a New Generalization of Bernstein-Type Rational Functions and Its Approximation

Abstract

In this study, we introduce a new generalization of a Bernstein-type rational function possessing better estimates than the classical Bernstein-type rational function. We investigate its error of approximation globally and locally in terms of the first and second modulus of continuity and a class of Lipschitz-type functions. We present graphical comparisons of its approximation with illustrative examples.

Keywords

• linear positive operator
• rate of convergence
• Bernstein-type rational function