# $\alpha$-optimal best proximity point result involving proximal contraction mappings in fuzzy metric spaces

Volume 10, Issue 1, pp 92--103
Publication Date: January 26, 2017 Submission Date: August 31, 2016
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### Authors

Abdul Latif - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Naeem Saleem - Department of Mathematics, University of Management and Technology, C-II, Johar Town, Lahore , Pakistan. Mujahid Abbas - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. - Department of Mathematics, University of Management and Technology, C-II, Johar Town, Lahore , Pakistan.

### Abstract

In this paper, we introduce $\alpha$-proximal fuzzy contraction of type-I and II in complete fuzzy metric space and obtain some fuzzy proximal and optimal coincidence point results. The obtained results further unify, extend and generalize some already existing results in literature. We also provide some examples which show the validity of obtained results and a comparison is also given which shows that contractive mappings and obtained results further generalizes already existing results in literature.

### Share and Cite

##### ISRP Style

Abdul Latif, Naeem Saleem, Mujahid Abbas, $\alpha$-optimal best proximity point result involving proximal contraction mappings in fuzzy metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 1, 92--103

##### AMA Style

Latif Abdul, Saleem Naeem, Abbas Mujahid, $\alpha$-optimal best proximity point result involving proximal contraction mappings in fuzzy metric spaces. J. Nonlinear Sci. Appl. (2017); 10(1):92--103

##### Chicago/Turabian Style

Latif, Abdul, Saleem, Naeem, Abbas, Mujahid. "$\alpha$-optimal best proximity point result involving proximal contraction mappings in fuzzy metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 1 (2017): 92--103

### Keywords

• Fuzzy metric space
• $\alpha$-proximal fuzzy contraction of type-I
• $\alpha$-proximal fuzzy contraction of type-II
• fuzzy expansive mapping
• optimal coincidence best proximity point
• t-norm.

•  47H10
•  47H04
•  47H07

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