Abstract
In this present study, we introduce the new class of mappings called fuzzy proximally compatible mappings and we solve the common coupled global optimization problem of finding the fuzzy distance between two subsets of a fuzzy metric space for this class of non-self-fuzzy mappings. Further, we develop the notion CLRg property (CLRg common limit in the range of g) for non-self-fuzzy mappings, and by having this idea, we derive common global minimal solution to the fuzzy coupled fixed point equations \(F(x,y) = g(x) = x\) and \(F(y,x) = g(y) = y,\) where the pair (F, g) is proximally fuzzy weakly compatible mappings, without the assumption of continuity on g. Finally, we find a relation between, our extended notions, proximal fuzzy E.A property and proximal fuzzy CLRg property, and we find a unique solution to the common global optimization problem with the assumption of proximal fuzzy E.A property.
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Acknowledgements
The authors would like to thank the National Board for Higher Mathematics (NBHM), DAE, Government of India, for providing a financial support under the Grant No. 02011/22/2017/R&D II/14080.
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Gopi, R., Pragadeeswarar, V. Determining fuzzy distance via coupled pair of operators in fuzzy metric space. Soft Comput 24, 9403–9412 (2020). https://doi.org/10.1007/s00500-020-05001-8
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DOI: https://doi.org/10.1007/s00500-020-05001-8