Mixed monotone operators and their application to integral equations

被引：10
|
作者：
Wardowski, Dariusz [1 ]
机构：
[1] Univ Lodz, Dept Nonlinear Anal, Fac Math & Comp Sci, Banacha 22, PL-90238 Lodz, Poland
来源：
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2017年 / 19卷 / 02期
关键词：
(e; u)-concave-convex operator; fixed point; mixed monotone operator; nonlinear integral equation; existence and uniqueness of a solution; COUPLED FIXED-POINTS; EXISTENCE; UNIQUENESS;
D O I：
10.1007/s11784-016-0335-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the mixed monotone operators of a new type in a Cartesian product of a Banach space with an order determined by a normal cone. We establish sufficient conditions for such operators to have a unique fixed point and provide monotone iterative techniques which give sequences convergent to the fixed point. We also apply the obtained results to prove the existence and uniqueness of a solution of a nonlinear integral equation.
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页码：1103 / 1117
页数：15
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