Best proximity point results for generalized contractions in metric spaces

Fixexd point theory and applications

Farhana Akbar¹  Nawab Hussain²  Alireza Amini-Harandi³ 

[1] Department of Mathematics, GDCW, Multan, Pakistan;Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;Department of Pure Mathematics, University of Shahrekord, Shahrekord, Iran

关键词: optimal solution;    best proximity point;    cyclic generalized contraction map;    proximal generalized contraction;    metric space;    uniformly convex Banach space;   

DOI  :  10.1186/1687-1812-2013-164

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we first introduce a cyclic generalized contraction map in metric spaces and give an existence result for a best proximity point of such mappings in the setting of a uniformly convex Banach space. Then we give an existence and uniqueness best proximity point theorem for non-self proximal generalized contractions. Moreover, an algorithm is exhibited to determine such a unique best proximity point. Some examples are also given to support our main results. Our results extend and improve certain recent results in the literature. MSC: 46N40, 47H10, 54H25, 46T99.

【 授权许可】

CC BY