On Almost Regular Convergence

Abstract

Regular convergence of multiple sequences, introduced by G. H. Hardy and F. Moricz, can be generalized to almost convergent sequences in various ways. In the paper, classes of almost convergent double sequences with a kind of uniform regularity are studied, which make these classes similar to the class of regularly convergent sequences. Matrices, which convert sequences from these classes to bounded and convergent double sequences with limits equal to the generalized limits of the original sequences are characterized. The results extend results of F. Moricz and B. E. Rhoades on strongly regular matrices.