q-Laguerre type linear positive operators

Abstract

The main object of this paper is to define the q-Laguerre type positive linear operators and investigate the approximation properties of these operators. The rate of convegence of these operators are studied by using the modulus of continuity, Peetre's K-functional and Lipschitz class functional. The estimation to the difference vertical bar M-n+1,M-q(f; x) - M-n,M-q(f; x) vertical bar is also obtained for the Meyer-Konig and Zeller operators based on the q-integers [2]. Finally, the r-th order generalization of the q-Laguerre type operators are defined and their approximation properties and the rate of convergence of this r-th order generalization are also examined.