Best proximity results: optimization by approximate solutions.
- Resource Type
- Article
- Authors
- Choudhury, Binayak; Metiya, Nikhilesh; Maniu, Georgeta; Konar, Pulak
- Source
- Fixed Point Theory & Applications. 7/15/2016, Vol. 2016 Issue 1, p1-13. 13p.
- Subject
- *PROXIMITY spaces
*MATHEMATICAL optimization
*APPROXIMATION theory
*CONTRACTIONS (Topology)
*MATHEMATICAL mappings
*GENERALIZATION
- Language
- ISSN
- 1687-1820
In this paper we utilize a generalized weakly contractive mapping to establish some best proximity point results which are global optimization results for finding the minimum distances between two sets. Amongst many approaches to this problem, we adopt the approach where the problem is treated as that of finding global optimal approximate solution of the fixed point equation for the generalized weak contraction mapping. We use three control functions to define such mappings. The results are obtained in metric spaces with a partial ordering defined therein. There is a blending of analytic and order theoretic approaches in the proofs. The uniqueness is obtained by imposing some order theoretic conditions additionally. There are several corollaries. An illustration of the main theorem through an example is given which also shows that the corollaries are properly contained in the main theorem. [ABSTRACT FROM AUTHOR]