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.
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