The Buck-Pollard Property forp-Cesàro Matrices

Abstract

Establishing a one-to-one correspondence between the interval (0, 1] and the collection of all subsequences of a given sequence s n , Buck and Pollard proved that s n is (C , 1)-summable if almost all of subsequences are, but not conversely. In this article, we consider the analogous questions for the p-Cesàro matrices. We show, for example, that if p > 1 2 then a bounded sequence is C p -summable if and only if almost all of its subsequences are C p -summable.

Characterization of q-Cesàro convergence for double sequences

“…The Buck-Pollard property is related to the convergence or summability of subsequences of a given sequence. Taking into consideration q-Cesàro matrix instead of (C, 1) matrix, similar results have been investigated in [7]. Recently the Buck-Pollard property for (C, 1, 1) summability method has been examined and also provided a new characterization of (C, 1, 1) summability for double sequences with respect to its subsequences [10].…”