On the Chlodowsky variant of Jakimovski-Leviatan-Paltanea Operators

Abstract

In the present paper, our purpose is to generalize the Jakimovski-Leviatan-Paltanea operators in the sense of Chlodowsky. After introducing the new operators we first obtain the moments of these operators in order to establish the convergency properties with the help of Korovkin's theorem. After that, we give the local approximation result and the Voronovskaya type theorem. We also examine the convergence properties of the operators in the weighted space of functions. Lastly we determine the rate of convergence of the operators with the aid of the weighted modulus of continuity.