Abstract
In Chapter 5, the matrix transformations between double sequence spaces are studied, Mercerian theorem and Steinhaus type theorems for four dimensional matrices are given. Also, the necessary and sufficient conditions for a four dimensional RH-regular matrix A to be stronger than the RH-regular Riesz mean Rqt are given, the concept of four dimensional usual dual summability methods is defined and the corresponding results for four dimensional dual summability methods of the new sort are obtained.
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