Matrix transforms of ?-boundedness domains of the Zweier method

Abstract

In this paper, we find necessary and sufficient conditions for the Zweier matrix method Z1/2 to be transform from the spaces of ?-bounded and ?-convergent sequences into the spaces of µ-bounded and µ-convergent sequences, where ? and µ are monotonically increasing sequences with positive entries (i.e. speeds). Also we find necessary and sufficient conditions for a matrix M to be transform from the ?-boundedness domain of Z1/2 into the µ-boundedness domain of a triangular matrix method B. In addition, we introduce one class of multiplicative matrices M satisfying these necessary and sufficient conditions.