Abstract
In the setting of fuzzy metric spaces (FMSs), a global optimization problem (GOP) obtaining the distance between two subsets of an FMS is solved by a tripled fixed-point (FP) technique here. Also, fuzzy weak tripled contractions (WTCs) for that are given. This problem was known before in metric space (MS) as a proximity point problem (PPP). The result is correct for each continuous τ—norms related to the FMS. Furthermore, a non-trivial example to illustrate the main theorem is discussed.
Highlights
Introduction and PreliminariesDuring the last decade, the proximity point problem (PPP) has been discussed as it means determining the distance between two subsets of the metric space (MS)
This problem is mainly considered and it is treated by FP analysis by viewing the problem as that of finding an optimal approximate solution of an FP equation, this problem was known as a global optimization problem (GOP)
Main Results We begin this section with the definition below
Summary
The PPP has been discussed as it means determining the distance between two subsets of the MS. In optimization, this problem is mainly considered and it is treated by FP analysis by viewing the problem as that of finding an optimal approximate solution of an FP equation, this problem was known as a GOP. Choudhury and Maity [11], obtained coupled proximity points in general FMSs. The goal of this work is to consider the global GOP of obtaining the distance between two subsets of an FMS and solve it by FP methodology through the determination of two different pairs of points each of which determines the fuzzy distance for which we use a tripled mapping from one set to the other
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