Existence and uniqueness of fixed points for monotone operators in partially ordered Banach spaces and applications

被引：0
作者：
Mohamed Khazou
Mohamed Aziz Taoudi
机构：
[1] Cadi Ayyad University,National School of Applied Sciences
来源：
Journal of Fixed Point Theory and Applications | 2021年 / 23卷
关键词：
Partially ordered Banach spaces; measures of weak noncompactness; fixed points; coupled fixed points; mixed monotone mappings; iterative techniques; differential equations; integral equations; 47H10; 47H07; 34B15; 34C12; 45N05;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper, we employ partial order method, cone theory, and the techniques of measure of weak noncompactness to prove several new theorems on the existence and the uniqueness of fixed points or coupled fixed points for operators satisfying some monotonicity assumptions. Our conclusions generalize and improve several well-known results. As an application, we investigate the existence of a unique solution for a class nonlinear second-order ordinary differential equations. We also discuss the existence of a unique solution for a system of integral equations.
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