Existence of local fractional integral equation via a measure of non-compactness with monotone property on Banach spaces

被引：0
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作者：
Hemant Kumar Nashine
Rabha W. Ibrahim
Ravi P. Agarwal
N. H. Can
机构：
[1] Vellore Institute of Technology,Department of Mathematics, School of Advanced Sciences
[2] University of Johannesburg,Department of Mathematics and Applied Mathematics
[3] Ton Duc Thang University,Informetrics Research Group
[4] Ton Duc Thang University,Faculty of Mathematics and Statistics
[5] Texas A&M University,Department of Mathematics
[6] Ton Duc Thang University,Applied Analysis Research Group, Faculty of Mathematics and Statistics
来源：
Advances in Difference Equations | / 2020卷
关键词：
Measure of non-compactness; Local fractional integral equation; 35F25; 45N05; 47H10;
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摘要：
In this paper, we discuss fixed point theorems for a new χ-set contraction condition in partially ordered Banach spaces, whose positive cone K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{K}$\end{document} is normal, and then proceed to prove some coupled fixed point theorems in partially ordered Banach spaces. We relax the conditions of a proper domain of an underlying operator for partially ordered Banach spaces. Furthermore, we discuss an application to the existence of a local fractional integral equation.
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