A new mathod for coupled best proimity point theorems in partially ordered metric spaces

DOI

10.2991/meic-14.2014.43How to use a DOI?

Keywords

coupled best proximity point; generalized contraction; weak P-monotone property; xed point.; contraction

Abstract

Several problems can be changed as equations of the form Tx = x, where T is a given self-mapping defined on a subset of a metric space, a normed linear space, a topological vector space or some suitable space. However, if T is a non-self mapping from A to B, then the aforementioned equation does not necessarily admit a solution. In this case, it is contemplated to find an approximate solution x in A such that the error d(x, Tx) is minimum, where d is the distance function. In view of the fact that d(x,Tx) is at least d(A,B), a best proximity point theorem guarantees the global minimization of d(x, Tx) bythe requirement that an approximate solution x satisfies the condition d(x, Tx) = d(A,B). Such optimal approximate solutions are called best proximity points of the mapping T. Interestingly, best proximity point theorems also serve as a natural generalization of fixed point theorems, for a besproximity point becomes a fixed point if the mapping under consideration is a self mapping. Research on the best proximity point is an important topic in the nonlinear functional analysis and applications. The aim of this paper is to obtain the coupled best proximity point theorems for generalized contraction in partially ordered metric spaces by P-operator technique. An example has also been given to support the usability of our results. Many recent results in this area have been improved.

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Sumei Ai
AU  - Yongfu Su
PY  - 2014/11
DA  - 2014/11
TI  - A new mathod for coupled best proimity point theorems in partially ordered metric spaces
BT  - Proceedings of the 2014 International Conference on Mechatronics, Electronic, Industrial and Control Engineering
PB  - Atlantis Press
SP  - 192
EP  - 195
SN  - 2352-5401
UR  - https://doi.org/10.2991/meic-14.2014.43
DO  - 10.2991/meic-14.2014.43
ID  - Ai2014/11
ER  -