International Journal of Analysis and Applications (Aug 2016)
Approximation Theorems for q- Analouge of a Linear Positive Operator by A. Lupas
Abstract
The purpose of the present paper is to introduce $q-$ analouge of a sequence of linear and positive operators which was introduced by A. Lupas [2]. First, we estimate moments of the operators and then prove a basic convergence theorem. Next, a local direct approximation theorem is established. Further, we study the rate of convergence and point-wise estimate using the Lipschitz type maximal function.