A New Kantorovich-Type Rational Operator and Inequalities for Its Approximation

Abstract

We introduce a new Kantorovich-type rational operator. We investigate inequalities estimating its rates of convergence in view of the modulus of continuity and the Lipschitz-type functions. Moreover, we present graphical comparisons exemplifying concretely its better approximation for a certain function. The results of the paper are crucial by means of possessing at least better approximation results than an existing Kantorovich-type rational function.

Keywords

• approximation of positive operators
• rate of convergence
• Kantorovich-type operator
• rational function