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Mathematics 2017, 5(2), 22; doi:10.3390/math5020022

On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces

1
Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, P.O. Box 644 de Bilbao, Barrio Sarriena, 48940 Leioa (Bizkaia), Spain
2
Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3
Department of Mathematics, Government College University, 54000 Lahore, Pakistan
4
Department of Mathematics, National University of Computer and Emerging Sciences, Milaad Street, Lahore 54000, Pakistan
5
Department of Mathematics, University of Management and Technology, C-II Johar Town, Lahore 54000, Pakistan
*
Author to whom correspondence should be addressed.
Academic Editor: Pasquale Vetro
Received: 30 March 2016 / Revised: 24 March 2017 / Accepted: 27 March 2017 / Published: 1 April 2017
(This article belongs to the Special Issue Fixed Point Theorems and Applications)
View Full-Text   |   Download PDF [330 KB, uploaded 10 April 2017]

Abstract

The main objective of this paper is to deal with some properties of interest in two types of fuzzy ordered proximal contractions of cyclic self-mappings T integrated in a pair ( g , T ) of mappings. In particular, g is a non-contractive fuzzy self-mapping, in the framework of non-Archimedean ordered fuzzy complete metric spaces and T is a p -cyclic proximal contraction. Two types of such contractions (so called of type I and of type II) are dealt with. In particular, the existence, uniqueness and limit properties for sequences to optimal fuzzy best proximity coincidence points are investigated for such pairs of mappings. View Full-Text
Keywords: fixed points; best proximity points; fuzzy set; fuzzy metric; optimal fuzzy best proximity coincidence points; proximal ψ-contractions of types I and II fixed points; best proximity points; fuzzy set; fuzzy metric; optimal fuzzy best proximity coincidence points; proximal ψ-contractions of types I and II
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. (CC BY 4.0).

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Sen, M.D.; Abbas, M.; Saleem, N. On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces. Mathematics 2017, 5, 22.

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