Parametric generalization of the modified Bernstein operators

Abstract

The current paper deals with the parametric modification of Bernstein operators which preserve constant and Korovkin’s other test functions in limit case. The uniform convergence of the newly constructed operators is studied. Also, the rate of convergence is investigated by means of the modulus of continuity and by the help of Peetre-K functionals. Finally, some numerical examples are given to illustrate the effectiveness of the newly defined operators for computing function approximation.