WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
Matrix Transforms into a Set of α-absolutely $$Α^λ$$-summable Sequences
Authors: ,
Abstract: Suppose A is a matrix having real or complex entries and λ- a monotonically increasing strictly positive sequence, i.e., the speed. In this paper, the notions of λ-reversibility of A,
$$Α^λ$$-boundedness, and $$Α^λ$$-summability of sequences are recalled, and the notion of α-absolute $$Α^λ$$-summability of sequences is introduced. Also, there are characterized matrix transforms from the set of all $$Α^λ$$ -bounded, or the set of all α-summable, or the set of all 1- absolute $$Α^λ$$-summable sequences into the set of all α-absolutely (α>1) $$Β^μ$$-summable sequences for a normal or λ-reversible matrix A and a matrix $$Β=(b_{nk})$$ with $$b_{nk}=0$$, k>n, and for another speed μ.
Search Articles
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
Pages: 891-897
DOI: 10.37394/23206.2024.23.92