Existence of best proximity points for controlled proximal contraction

Fixexd point theory and applications

Erdal Karapı¹  Tayyab Kamran²  Muhammad Usman Ali²  Quanita Kiran³ 

[1] Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan;Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan;School of Electrical Engineering and Computer Sciences, National University of Sciences and Technology, Islamabad, Pakistan

关键词: Point Theorem;    Closed Subset;    Fixed Point Theorem;    Contraction Condition;    Contraction Mapping;   

DOI  :  10.1186/s13663-015-0455-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we investigate the sufficient condition for the existence of best proximity points for non-self-multivalued mappings. Additionally, we discuss the stability theorem for such mappings. Our results improve and generalize some existing results on the topic in the literature, in particular, the results of Lim and of Abkar and Gabeleh.

【 授权许可】

CC BY