Abstract
This article is the forward result of α-admissible and (α,ψ)-contractive mappings in fuzzy metric spaces. We establish new theorem for such contractions to find fixed point in fuzzy metric space. Our Theorem is generalizations of some interesting outputs in metric spaces. Moreover, an example and application to ordinary differential equations are also elaborated to verify the result of the theorem.
Highlights
Nature of work on ...xed point theory are versatile and always have been source of motivation for further research
Kramosil and Michalek [3] prefaced the concept of fuzzy metric space using continuous t-norm and probabilistic metric space in 1975
A modi...cation of this result was done by George and Veeramani [2] which is used more frequently to ...nd ...xed point in fuzzy metric space
Summary
Nature of work on ...xed point theory are versatile and always have been source of motivation for further research. Gregori and Sapena [8] have explained Banach contraction principle in complete fuzzy metric space. A modi...cation of this result was done by George and Veeramani [2] which is used more frequently to ...nd ...xed point in fuzzy metric space. Salimi [10] modi...ed the belief of ( ; )-contractive and -admissible mapping to get ...xed point theorem in complete metric space. In 2014, Hong [11] introduced ( ; )- contraction for set-valued mapping in fuzzy metric space. Many other authors contributed their research to give direction in the ...eld of fuzzy metric space [13, 14, 15, 16, 17, 18] C 2018 Ankara University C om munications Faculty of Sciences U niversity of A nkara-Series A 1 M athem atics and Statistics our e¤orts to prove our result using ( ; )-contraction mapping and -admissible mapping in fuzzy metric space
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