Existence and uniqueness of fixed points for mixed monotone operators with applications

被引：42
作者：
Wu, Yuexiang [1 ]
Liang, Zhandong
机构：
[1] Shanxi Univ Finance & Econ, Dept Appl Math, Shanxi 030006, Peoples R China
[2] Shanxi Univ Finance & Econ, Coll Math Sci, Shanxi 030006, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2006年 / 65卷 / 10期
基金：
中国国家自然科学基金;
关键词：
mixed monotone operators; cone and semiorder; fixed point;
D O I：
10.1016/j.na.2005.10.045
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the uniqueness and existence of fixed points of mixed monotone operators in the partially ordered Banach space. Our conclusions essentially improve the relevant results obtained by Liang and others. Moreover, as an application of our results, we prove the existence and uniqueness of a positive solution for a class of integral equations which cannot be solved by using previously available methods. (c) 2006 Published by Elsevier Ltd.
引用
收藏
页码：1913 / 1924
页数：12
相关论文
共 14 条
[1]  
AMANN H, 1976, SIAM REV, V18, P621
[2]   FUNDAMENTAL PROPERTIES OF A BANACH SPACE WITH A CONE [J].
ANDO, T .
PACIFIC JOURNAL OF MATHEMATICS, 1962, 12 (04) :1163-&
[3]  
Deimling K., 2010, NONLINEAR FUNCTIONAL, DOI DOI 10.1007/978-3-662-00547-7
[4]   COUPLED FIXED-POINTS OF NONLINEAR OPERATORS WITH APPLICATIONS [J].
GUO, D ;
LAKSHMIKANTHAM, V .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1987, 11 (05) :623-632
[5]  
Guo D, 1992, APPL ANAL, V46, P91, DOI [10.1080/00036819208840113, DOI 10.1080/00036819208840113]
[6]  
Guo D., 1988, NONLINEAR PROBLEMS A
[7]  
Guo D., 2000, Partial Order Method in Nonlinear Analysis
[8]  
Krasnoselskii M. A., 1984, GEOMETRICAL METHODS
[9]  
Liang Z.D., 1996, ACTA MATH SIN CHINES, V39, P204
[10]  
Liang ZD, 2003, Z ANAL ANWEND, V22, P529
12