@article{Ishtiaq2023, 
author = {Umar Ishtiaq and Fahad Jahangeer and Doha A. Kattan and Manuel De la Sen},
title = {Generalized common best proximity point results in fuzzy multiplicative metric spaces},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {25454-25476},
keywords = {fuzzy multiplicative metric space, fixed-point, best proximity point theorems, contraction mappings, uniqueness},
url = {https://www.sciopen.com/article/10.3934/math.20231299},
doi = {10.3934/math.20231299},
abstract = {In this manuscript, we prove the existence and uniqueness of a common best proximity point for a pair of non-self mappings satisfying the iterative mappings in a complete fuzzy multiplicative metric space. We consider the pair of non-self mappings    X  :      P    →      G   and    Z  :      P    →      G   and the mappings do not necessarily have a common fixed-point. In a complete fuzzy multiplicative metric space, if        φ   satisfy the condition        φ        (          b      ,      Z      b      ,      ς        )    =      φ        (                  P            ,              G            ,      ς        )    =      φ        (          b      ,      X      b      ,      ς        )  , then    b is a common best proximity point. Further, we obtain the common best proximity point for the real valued functions        L    ,      M    :  (  0  ,  1  ]  →      R   by using a generalized fuzzy multiplicative metric space in the setting of    (      L    ,      M    )-iterative mappings. Furthermore, we utilize fuzzy multiplicative versions of the    (      L    ,      M    )-proximal contraction,    (      L    ,      M    )-interpolative Reich-Rus-Ciric type proximal contractions,    (      L    ,      M    )-Kannan type proximal contraction and    (      L    ,      M    )-interpolative Hardy-Rogers type proximal contraction to examine the common best proximity points in fuzzy multiplicative metric space. Moreover, we provide differential non-trivial examples to support our results.}
}