q-Cesaro matrix and q-statistical convergence

Abstract

It is obvious that a q-analog of C-alpha, the Cesaro matrix of order alpha, can be defined in different ways. In this paper we introduce a method to find q-analogs of C-alpha, where alpha is a positive integer. Using this method, we obtain the most natural q-analogs of C-alpha. We also prove that the strength of C-1 (q(k)) does not depend on q, where C-1 (q(k)) is the most natural q-analog of C-1. Finally, we define a density function and q-statistical convergence using C-1 (q(k)). (C) 2010 Elsevier B.V. All rights reserved.