qq-Cesáro matrix and qq-statistical convergence

It is obvious that a qq-analog of CαCα, the Cesáro matrix of order αα, can be defined in different ways. In this paper we introduce a method to find qq-analogs of CαCα, where αα is a positive integer. Using this method, we obtain the most natural qq-analogs of CαCα. We also prove that the strength of C1(qk)C1(qk) does not depend on qq, where C1(qk)C1(qk) is the most natural qq-analog of C1C1. Finally, we define a density function and qq-statistical convergence using C1(qk)C1(qk).