Operators associated with adjoint Bernoulli polynomials

Abstract

Very recently Yilmaz [12] proposed Kantorovich type operators based on adjoint Bernoulli polynomials. She considered the operators on the finite interval [0, 1], but we observe here that these operators can be defined on positive real axis. We estimate moments using the technique of moment generating functions. We also obtain some direct results for these operators. Also we consider composition of these operators with well known Sz´asz-Mirakjan operators and estimate some direct convergence estimates.