On some measures of noncompactness in the Fréchet spaces of continuous functions
type: Item
instance of: scholarly article
title: On some measures of noncompactness in the Fréchet spaces of continuous functions
zbMATH Open document ID: 1179.45007
author: Leszek Olszowy
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-10-09T00:00:00Z
review text: The paper is devoted to construction of new regular measures of noncompactness for Fréchet spaces of continuous functions on a bounded or an unbounded interval. For those spaces several properties of these new measures are established. The results obtained are further applied to infinite systems of functional integral equations of the form \[ x^i(t)=f_i\left( t,x^i(t),\int_{0}^{t}u_i(t,\tau,x^1(\tau),x^2(\tau),\dots)d\tau \right) \] where \( i=1,2,\dots \) and \(t\in \mathbb{R}_+\). It is proved that under some assumptions this infinite system has at least one solution \(x(t)=(x^i(t))\) such that \(x(t)\) belongs to Fréchet space \(C(\mathbb{R}_+,s)\).
reviewed by: Alexander N. Tynda
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 5612944
zbMATH Keywords: infinite system of integral equations
zbMATH Keywords: Fréchet space
zbMATH Keywords: measures of noncompactness
zbMATH Keywords: Tikhonov fixed point principle
MaRDI profile type: Publication
full work available at URL: j.na.2009.03.083
OpenAlex ID: W2041851429
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DOI: 10.1016/J.NA.2009.03.083
description: scientific article; zbMATH DE number 5612944