Approximation by q-analogue of modified Jakimovski-Leviatan-Stancu type operators

Abstract

In this paper, we introduce the q-analogue of the Jakimovski-Leviatan type modified operators introduced by Atakut with the help of the q-Appell polynomials.We obtain some approximation results via the well-known Korovkin’s theorem for these operators.We also study convergence properties by using the modulus of continuity and the rate of convergence of the operators for functions belonging to the Lipschitz class. Moreover,we study the rate of convergence in terms of modulus of continuity of these operators in aweighted space.

Keywords

• q-analogue of Jakimovski-Leviatan operators
• modulus of continuity
• rate of approximation
• K-functional
• weighted spaces
• 41A10
• 41A25
• 41A36