WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
Matrix Transforms of $$α$$-absolutely $$A^{λ}$$-summable Sequences
Authors: ,
Abstract: Let $$A$$ be a matrix with real or complex entries, $$λ$$- a monotonically increasing strictly positive sequence, i.e., the speed of convergence, and $$α$$- a positive real number. In this paper, the notions of $$λ$$-reversibility of A, $$A^{λ}$$-boundedness, $$A^{λ}$$-summability and $$α$$-absolute $$A^{λ}$$-summability of sequences are recalled. Also necessary and sufficient conditions for a matrix M (with real or complex entries) to map the set of all $$α$$-absolutely $$A^{λ}$$-summable sequences into the set of all $$β$$-absolutely $$Β^{μ}$$ -summable sequences, or into the set of all $$Β^{μ}$$-bounded or $$Β^{μ}$$-summable sequences, if A is a normal or λ-reversible matrix, $$B$$– a lower triangular matrix, $$μ$$- another speed of convergence and $$0<α\leqβ\leq1$$. As an application, we consider the case when A is the Zweier matrix $$Ζ_{\frac{1}{2}} $$
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Keywords: Matrix transforms, $$λ$$-reversibility of matrices, boundedness with speed, convergence with speed, zero-convergence with speed, summability with speed, $$α$$-absolute summability with speed, Zweier matrix
Pages: 836-847
DOI: 10.37394/23206.2024.23.86