A new generalization of Szasz-Kantorovich operators on weighted space

Abstract

The purpose of this article is to define a new generalization of Szász-Kantorovich operators. First, by using the Korovkin theorem on the new operator we define, its convergence properties and rates are examined. Then, the Voronovskaja-type theorem for the new operator is proven. Additionally, with the help of the modulus of continuity in the weighted space, rate of convergence the new operator is examined, and a theorem is proven for the operator we define by using functions that satisfy the Lipschitz condition. Finally, the convergence is demonstrated more clearly by numerical examples and plots.