Absolute Summability by Series-to-Sequence Transformation Matrices

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Communications Faculty of Sciences University Ankara Series A2-A3 Physical and Engineering
Volume:23
Absolute Summability by Series-to-Sequence Transformation Matrices

Absolute Summability by Series-to-Sequence Transformation Matrices

Authors : M B ZAMAN

Pages : 0-0

View : 40 | Download : 7

Publication Date : 1974-01-01

Article Type : Research Paper

Abstract :n this paper we define an absolute summability by a series-to-sequence transfor mation matrix. We obtain tbe necessary and sufficient conditions in order that every absolutely convergent series is absolutely summable by series-to-sequence transfor mation matrix. For this we find new classes of matrices-conservative series-to-sequence transformation matrices and regular series-to-sequence transformation matrices. We study the relation of these two new classes of matrices with K, p,T and y-matrices. Finally we prove that the absolute summability of an absolutely convergent series by a matrix and the generalized limit of its absolute partial sum are equal under the suitable relation between the two matrices.
Keywords : science, Absolute, Matrices

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