Generalization of Szász operators: quantitative estimate and bounded variation

Abstract

Difference of exponential type Szász and Szász-Kantorovich operators is obtained. Similar estimates are given for higher order $\mu$-derivatives of the Szász operators and the Szász-Kantorovich type operators acting on the same order $\mu$-derivative of the function. These differences are given in quantitative form using the first modulus of continuity. Convergence in variation of the operators in the space of functions with bounded variation with respect to the variation seminorm is obtained. The results propose a general framework covering the results provided by previous literature.