q-Cesáro matrix and q-statistical convergence

摘要

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