Optimal coincidence points of proximal quasi-contraction mappings in non-Archimedean fuzzy metric spaces

Volume 9, Issue 6, pp 3787--3801 http://dx.doi.org/10.22436/jnsa.009.06.28

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Authors

Zahid Raza - Department of Mathematics, National University of Computer and Emerging Sciences, Lahore, Pakistan. - Department of Mathematics, University of Sharjah, Sharjah, UAE. Naeem Saleem - Department of Mathematics, National University of Computer and Emerging Sciences, Lahore, Pakistan. Mujahid Abbas - Department of Mathematics, University of Pretoria, South Africa. - Department of Mathematics, King Abdulaziz University, P. O. Box. 80203, Jeddah 21589, Saudi Arabia.

Abstract

The aim of this paper is to present fuzzy optimal coincidence point results of fuzzy proximal quasi contraction and generalized fuzzy proximal quasi contraction of type-1 in the framework of complete non- Archimedean fuzzy metric space. Some examples are presented to support the results which are obtained here. These results also hold in fuzzy metric spaces when some mild assumption is added to the set in the domain of mappings which are involved here. Our results unify, extend and generalize various existing results in literature.

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Keywords

• Fuzzy metric space
• fuzzy proximal
• quasi contractions
• fuzzy expansive mapping
• optimal coincidence best proximity point
• t-norm.

MSC

•  47H10
•  47H04
•  47H07

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