Characterization of q-Cesaro convergence for double sequences

Abstract

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