In this paper,we prove a theorem which gives an equivalent formulation of summability by weighted mean methods. The result of Hardy [1] and that of Móricz and Rhoades [2] are special cases of this theorem. In this context, it is important to note that the result of Móricz and Rhoades is valid even without the assumption \(\frac{p_n}{P_n}\to0\) as \(n\to\infty\).
In this short paper, \(K\) denotes a complete, non-trivially valued, ultrametric field. Sequences and infinite matrices have entries in K. We prove a few characterizations of Schur matrices in \(K\). We then deduce some non-inclusion theorems modelled on the results of Agnew [1] and Fridy [3] in the classical case.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.