Optimal Coincidence Best Approximation Solution in b-fuzzy Metric Spaces

Document Type: Original Article


1 Department of Mathematics, Government College University,Lahore 54000, Pakistan.

2 Department of Mathematics, University of Management and Technology, Lahore, Pakistan


In this paper, we prove the existence of optimal coincidence point and best proximity point in b-fuzzy
metric space for two mappings satisfying certain contractive conditions and prove some proximal theorems
which provide the existence of an optimal approximate solution to some operator equations which are not
solvable. We also provide an application to the fi xed point theory of our obtained results.


[1]H. Alolaiyan, N. Saleem, M. Abbas, A natural selection of a graphic contraction transformation in fuzzy metric
spaces, J. Nonlinear Sci. Appl., 11 (2018), 218-227.

[2]I. A. Bakhtin, The contraction mapping principle in quasi-metric spaces, Funct. Anal. Ulianowsk, Gos. Ped. Inst.,
30 (1989), 26-37.

[3]S. Czerwik, Contraction mappings in b-metric space, Acta Math. Inf. Univ. Os-traviensis, 1 (1993), 5-11.

[4]T. Dosenovic, A. Javaheri, S. Sedghi, N. Shobe, Coupled fixed point theorem in b-fuzzy metric spaces, NOVI SAD
J. MATH., 47(1) (2017), 77-88.

[5]A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90(3)
(1997), 365-368.

[6]M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets, and Systems, 27(3) (1983), 385-389.

[7]V. Gregori, A. Sapena, On xed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125(2) (2002),

[8]N. Hussain, P. Salimi, V. Parvaneh, Fixed point results for various contractions in parametric and fuzzy b-metric
spaces, J. Nonlinear Sci. Appl., 8 (2015), 719-739.

[9]I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11(5) (1975), 336-344.

[10]S. Nadaban, Fuzzy b-metric spaces, International Journal of Computers Communications & Control, 11(2) (2016),

[11]Z. Raza, N. Saleem, M. Abbas, Optimal coincidence points of proximal quasi-contraction mappings in nonArchimedean
fuzzy metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 3787-3801.

[12]N. Saleem, M. Abbas, Z. Raza, Optimal coincidence best approximation solution in non-Archimedean fuzzy metric
spaces, Iranian Journal of fuzzy systems, 13(3) (2016), 113-124.

[13]B. Schweizer, A. Sklar, Statistical metric spaces, Paci c J.Math., 10(1) (1960), 313-334.

[14]S. Sedghi, N. Shobe, Common fixed point theorems in b-fuzzy metric spaces, Nonlinear Function Analysis and
Application, 17(3) (2012), 349-359.

[15]L. A. Zadeh, Fuzzy Sets, Informations and control, 8(3) (1965), 338-353.