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

被引：0

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;

D O I：

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中图分类号：

学科分类号：

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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