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

Fixexd point theory and applications

Cristina Urs¹  Gabriela Petruel¹  Adrian Petruel¹ 

[1] Babe-Bolyai University Cluj-Napoca, Cluj-Napoca, Romania

关键词: singlevalued operator;    multivalued operator;    vector-valued metric;    fixed point;    ordered metric space;    coupled fixed point;    Ulam-Hyers stability;    limit shadowing property;   

DOI  :  10.1186/1687-1812-2013-218

学科分类：数学（综合）

来源: SpringerOpen

【 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. MSC:47H10, 54H25.

【 授权许可】

CC BY