An extension of Darbo's theorem and its application
type: Item
instance of: scholarly article
title: An extension of Darbo's theorem and its application
zbMATH Open document ID: 1473.47018
DOI: 10.1155/2014/852324
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Here, some extensions of Darbo fixed point theorem associated with measures of noncompactness are proved. Then, as an application, our attention is focused on the existence of solutions of the integral equation \(x(t) = F(t, f(t, x(\alpha_1(t)),x(\alpha_2(t)))\), \(((T x)(t) / \Gamma(\alpha)) \times \int_0^t (u(t, s, \max_{[0, r(s)]} | x(\gamma_1(\tau)) |\), \(\max_{[0, r(s)]} | x(\gamma_2(\tau)) |)\)/\((t - s)^{1 - \alpha})\, d s\), \(\int_0^\infty v(t, s, x(t)) \,d s)\), \(0 < \alpha \leq 1\), \(t \in [0,1]\) in the space of real functions defined and continuous on the interval \([0,1]\).
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H08
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7023199
zbMATH Keywords: Darbo fixed point theorem
zbMATH Keywords: measures of noncompactness
zbMATH Keywords: integral equation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/852324
OpenAlex ID: W2091872833
Wikidata QID: Q59042049
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description: scientific article; zbMATH DE number 7023199