Some new sequence spaced defined by a modulus function
type: Item
instance of: scholarly article
title: Some new sequence spaced defined by a modulus function
zbMATH Open document ID: 0805.40004
author: Fatih Nuray
author: Ekrem Savaş
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1995-01-26T00:00:00Z
review text: Let \(\sigma: \mathbb{N}\to \mathbb{N}\) be an one-to-one mapping such that \(\sigma^ k (n)\neq n\) for all \(n\) and \(k\). Let \(f\) be a modulus function, and let \(A\) be a nonnegative regular matrix. The authors prove that \(w(A_ \sigma, f):= \{x= (x_ k)\mid \lim_ m \sum_ k a_{mk} f(| x_{\sigma^ \kappa(n)} -L|) =0\), for some \(L\) uniformly in \(n\}\) and \(w_ 0(A_ \sigma, f):= \{x\in w(A_ \sigma, f)\mid L=0\}\) are complete linear topological spaces paranormed by \(g(x):= \sup_{n,m} \sum_ k a_{mk} f(| x_{\sigma^ \kappa(n)} |)\).
Mathematics Subject Classification ID: 40A99
Mathematics Subject Classification ID: 40J05
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 40C05
zbMATH DE Number: 597304
zbMATH Keywords: modulus function
zbMATH Keywords: regular matrix
zbMATH Keywords: linear topological spaces
reviewed by: Toivo Leiger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 597304