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Abstract and Applied Analysis
Volume 2016, Article ID 9784592, 8 pages
http://dx.doi.org/10.1155/2016/9784592
Research Article

Best Proximity Point Theorem in Quasi-Pseudometric Spaces

Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Received 24 October 2015; Revised 17 December 2015; Accepted 20 December 2015

Academic Editor: Ngai-Ching Wong

Copyright © 2016 Robert Plebaniak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In quasi-pseudometric spaces (not necessarily sequentially complete), we continue the research on the quasi-generalized pseudodistances. We introduce the concepts of semiquasiclosed map and contraction of Nadler type with respect to generalized pseudodistances. Next, inspired by Abkar and Gabeleh we proved new best proximity point theorem in a quasi-pseudometric space. A best proximity point theorem furnishes sufficient conditions that ascertain the existence of an optimal solution to the problem of globally minimizing the error , and hence the existence of a consummate approximate solution to the equation .