Geodesic
$\alpha$-optimal best proximity point result involving proximal contraction mappings in fuzzy metric spaces
Latif, Abdul1 ; Saleem, Naeem2 ; Abbas, Mujahid3
1 Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2 Department of Mathematics, University of Management and Technology, C-II, Johar Town, Lahore , Pakistan
3 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
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 92-103.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.01.09
Classification : 47H10, 47H04, 47H07
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.

Latif, Abdul 1 ; Saleem, Naeem 2 ; Abbas, Mujahid 3

1 Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2 Department of Mathematics, University of Management and Technology, C-II, Johar Town, Lahore , Pakistan
3 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 
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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 its applications, Tome 10 (2017) no. 1, p. 92-103. doi : 10.22436/jnsa.010.01.09. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.01.09/

[1] Abbas, M.; Saleem, N.; Sen, M. De la Optimal coincidence point results in partially ordered non-Archimedean fuzzy metric spaces, Fixed Point Theory Appl., Volume 2016 (2016 ), pp. 1-18 | Zbl | DOI

[2] Sen, M. De la; Abbas, M.; N. Saleem On optimal fuzzy best proximity coincidence points of fuzzy order preserving proximal \((\alpha,\beta)\)-lower-bounding asymptotically contractive mappings in non-Archimedean fuzzy metric spaces , SpringerPlus, Volume 5 (2016), pp. 1-26 | DOI

[3] Eldred, A. A.; Veeramani, P. Existence and convergence of best proximity points , J. Math. Anal. Appl., Volume 323 (2006), pp. 1001-1006 | DOI

[4] Fan, K. Extensions of two fixed point theorems of F. E. Browder , Math. Z., Volume 112 (1969), pp. 234-240 | DOI

[5] George, A.; Veeramani, P. On some results in fuzzy metric spaces , Fuzzy Sets and Systems, Volume 64 (1994), pp. 395-399 | DOI

[6] George, A.; P. Veeramani On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, Volume 90 (1997), pp. 365-368 | DOI

[7] Grabiec, M. Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, Volume 27 (1988), pp. 385-389 | DOI

[8] García, J. Gutiérrez; Romaguera, S. Examples of non-strong fuzzy metrics, Fuzzy Sets and Systems, Volume 162 (2011), pp. 91-93 | DOI | Zbl

[9] Hussain, N.; Latif, A.; P. Salimi Best proximity point results for modified Suzuki \(\alpha-\psi\)-proximal contractions, Fixed Point Theory Appl., Volume 2014 (2014 ), pp. 1-16 | DOI | Zbl

[10] Jleli, M.; Samet, B. An optimization problem involving proximal quasi-contraction mappings, Fixed Point Theory Appl., Volume 2014 (2014 ), pp. 1-12 | Zbl | DOI

[11] Kramosil, I.; Michàlek, J. Fuzzy metric and statistical metric spaces, Kybernetika (Prague), Volume 11 (1975), pp. 336-344

[12] Latif, A.; Hezarjaribi, M.; Salimi, P.; Hussain, N. Best proximity point theorems for \(\alpha-\psi\)-proximal contractions in intuitionistic fuzzy metric spaces, J. Inequal. Appl., Volume 2014 (2014 ), pp. 1-19 | DOI | Zbl

[13] Latif, A.; Ninsri, A.; Sintunavarat, W. The \((\alpha,\beta)\)-generalized convex contractive condition with approximate fixed point results and some consequence, Fixed Point Theory Appl., Volume 2016 (2016 ), pp. 1-14 | Zbl | DOI

[14] Mongkolkeha, C.; Cho, Y. J.; Kumam, P. Best proximity points for generalized proximal C-contraction mappings in metric spaces with partial orders, J. Inequal. Appl., Volume 2013 (2013 ), pp. 1-12 | Zbl | DOI

[15] Mongkolkeha, C.; Sintunavarat, W. Best proximity points for multiplicative proximal contraction mapping on multiplicative metric spaces, J. Nonlinear Sci. Appl., Volume 8 (2016), pp. 1134-1140 | Zbl

[16] Ozavsar, M.; Cevikel, A. C. Fixed points of multiplicative contraction mappings on multiplicative metric spaces, ArXiv, Volume 2012 (2012), pp. 1-14

[17] Raza, Z.; Saleem, N.; Abbas, M. Optimal coincidence points of proximal quasi-contraction mappings in non-Archimedean fuzzy metric spaces, J. Nonlinear Sci. Appl., Volume 9 (2016), pp. 3787-3801 | Zbl

[18] Saleem, N.; Abbas, M.; Raza, Z. Optimal coincidence best approximation solution in non-Archimedean fuzzy metric spaces, Iran. J. Fuzzy Syst., Volume 13 (2016), pp. 113-124 | Zbl

[19] Saleem, N.; Ali, B.; Abbas, M.; Raza, Z. Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications, Fixed Point Theory Appl., Volume 2015 (2015 ), pp. 1-18 | Zbl | DOI

[20] Raj, V. Sankar; Veeramani, P. Best proximity pair theorems for relatively nonexpansive mappings, Appl. Gen. Topol., Volume 10 (2009), pp. 21-28 | DOI

[21] Schweizer, B.; Sklar, A. Statistical metric spaces, Pacific J. Math., Volume 10 (1960), pp. 313-334

[22] Suzuki, T.; Kikkawa, M.; Vetro, C. The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal., Volume 71 (2009), pp. 2918-2926 | Zbl | DOI

[23] Vetro, C.; Salimi, P. Best proximity point results in non-Archimedean fuzzy metric spaces, Fuzzy Inf. Eng., Volume 5 (2013), pp. 417-429 | DOI

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