Vector-valued metrics, fixed points and coupled fixed points for nonlinear operators

被引：15

作者：

Petrusel, Adrian ^{[1
]}

Petrusel, Gabriela ^{[1
]}

Urs, Cristina ^{[1
]}

机构：

[1] Univ Babes Bolyai, Cluj Napoca 400084, Romania

来源：

FIXED POINT THEORY AND APPLICATIONS | 2013年

关键词：

singlevalued operator; multivalued operator; vector-valued metric; fixed point; ordered metric space; coupled fixed point; Ulam-Hyers stability; limit shadowing property; MULTIVALUED OPERATORS; BANACH-SPACES; THEOREMS; STABILITY; SET;

D O I：

10.1186/1687-1812-2013-218

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we will present fixed point theorems for singlevalued and multivalued operators in spaces endowed with vector-valued metrics, as well as a Gnana Bhaskar-Lakshmikantham-type theorem for the coupled fixed point problem, associated to a pair of singlevalued operators (satisfying a generalized mixed monotone property) in ordered metric spaces. The approach is based on Perov-type fixed point theorems in spaces endowed with vector-valued metrics. The Ulam-Hyers stability and the limit shadowing property of the fixed point problems are also discussed.

引用

页数：21

共 37 条

[1] CONTRACTION AND APPROXIMATE CONTRACTION WITH AN APPLICATION TO MULTI-POINT BOUNDARY-VALUE-PROBLEMS [J].