Optimization Letters

, Volume 7, Issue 1, pp 145–155

Best proximity points: approximation and optimization

Original Paper

DOI: 10.1007/s11590-011-0404-1

Cite this article as:
Sadiq Basha, S., Shahzad, N. & Jeyaraj, R. Optim Lett (2013) 7: 145. doi:10.1007/s11590-011-0404-1

Abstract

A best proximity point theorem explores the existence of an optimal approximate solution, known as a best proximity point, to the equations of the form Tx = x where T is a non-self mapping. The purpose of this article is to establish some best proximity point theorems for non-self non-expansive mappings, non-self Kannan- type mappings and non-self Chatterjea-type mappings, thereby producing optimal approximate solutions to some fixed point equations. Also, algorithms for determining such optimal approximate solutions are furnished in some cases.

Keywords

Optimal approximate solution Fixed point Best proximity point Contraction Cyclic contraction Non-expansive map Kannan-type mapping Chatterjea-type mapping 

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsAnna UniversityChennaiIndia
  2. 2.Department of MathematicsKing Abdul Aziz UniversityJeddahSaudi Arabia
  3. 3.St. Joseph’s College Higher Secondary SchoolTrichyIndia