Characterization of q-Cesaro convergence for double sequences

Abstract

In the present paper we examine the Buck-Pollard property of 4 dimensional q-Cesaro matrices. Indeed we discuss some questions related to the q-Cesaro summability of subsequences of a given double sequence. The main result states that "a bounded double sequence is q-Cesaro summable to L if and only if almost all of its subsequences are q-Cesaro summable to 2(1-q) L".