Cesàro Means of Subsequences of Double Sequences - Taş, Emre; Orhan, Cihan (Sarajevo Journal of Mathematics, 2020)
In this paper we characterize the convergence and ( C,1,1) summability of a double sequence. In particular we study conditions under which the convergence or ( C,1,1) summability of a double sequence carry over to that of its subsequences, and conversely, whether these properties for suitable subsequences imply them for the sequence itself. We show, for instance, that a bounded double sequence is (C,1,1) summable if and only if almost all of its subsequences are ( C,1,1) summable.