\(r\)-convex sequences and matrix transformations
type: Item
instance of: scholarly article
title: \(r\)-convex sequences and matrix transformations
zbMATH Open document ID: 0847.40004
DOI: 10.1007/BF01874579
author: Z. U. Ahmad
author: Q. A. Khan
author: M. Mursaleen
published in: Acta Mathematica Hungarica
publication date: 1996-10-06T00:00:00Z
review text: By considering a fixed chosen sequence \(B= (Bi)= (b_{np} (i))\) of infinite matrices, the authors introduce the notion of \(F_B\) convergence as follows. \(x\in \ell_\infty\) is said to be \(F_B\) convergent to the \(\text{Lim } Bx\) if \[ \lim_{n\to \infty} (B_i x)_n= \lim_{n\to \infty} \sum_{p=0}^\infty b_{np} (i) x_p= \text{Lim } Bx \] uniformly in \(i= 0, 1, 2, 3, \dots\). The authors obtain necessary and sufficient conditions on the matrix \(A= (a_{nk})\) to transform \(\text{SC}^r\) and \(\ell_1\) to \(F_B\) where \(\text{SC}^r\) is the set of all \(r\)-convex sequences and \(\ell_1= \{(x_n): \sum^\infty_{n=0} |x_n |< \infty\}\).
Mathematics Subject Classification ID: 40C05
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 878107
zbMATH Keywords: matrix transformations
zbMATH Keywords: convergence
zbMATH Keywords: \(r\)-convex sequences
reviewed by: D. Somasundaram
MaRDI profile type: Publication
cites work: A contribution to the theory of divergent sequences
cites work: Q3994336
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full work available at URL: https://doi.org/10.1007/bf01874579
OpenAlex ID: W2023601168
description: scientific article; zbMATH DE number 878107