Background
Type: Article

Best proximity point results for generalized contractions in metric spaces

Journal: Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)Year: June 2012Volume: 2013Issue:
GoldDOI:10.1186/1687-1812-2013-164Language: English

Abstract

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. © 2013 Amini-Harandi et al.; licensee Springer.


Author Keywords

Best proximity pointCyclic generalized contraction mapMetric spaceOptimal solutionProximal generalized contractionUniformly convex Banach space