Approximation by Chlodowsky type Jakimovski–Leviatan operators

摘要

We introduce a generalization of the Jakimovski–Leviatan operators constructed by A. Jakimovski and D. Leviatan (1969) in [1]   and the theorems on convergence and the degree of convergence are established. We also give a Voronovskaya-type theorem. Furthermore, we study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity introduced by A.D. Gadjiev and A. Aral (2007) in [9].