A Theorem on Weighted Means in Non-Archimedean Fields

K denotes a complete, non-trivially valued, non-archimedean field. Infinite matrices, sequences and series have entries in K. In this paper, we prove an interesting result, which gives an equivalent formulation of summability by weighted mean methods. Incidentally this result includes the non-archimedean analogue of a theorem proved by Moricz and Rhoades (see [2], Theorem MR, p.188).