Jungck G & Rhoades B E, Fixed point for set valued functions without continuity, Indian J. Jha K, Karadzhov G E & Pecaric J, A generalized common fixed point in fuzzy metric space, The Nepali Math. Grabiec G, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27(1988), 385. George A & Veeramani P, On some results in fuzzy metric space, Fuzzy Sets and Systems, 64(1994), 395. Ĭho Y J, Pathak H K, Kang S M & Jung J S, Common fixed points of compatible mappings of type (B) on on fuzzy metric space, Fuzzy Sets and Systems, 93(1998), 99.Ĭhauhan M S, Badshah V M, & Chouhan V S, Common fixed point of semi-compatible maps in fuzzy metric space, Kath. (M(u, u0, t)) > M(u, u0, t), and hence, we get u = u0.īalasubramaniam P, Muralishankar S & Pant R P, Common fixed points of four mappings in a fuzzy metric space, J. įor an example: a * b = ab, a * b = min ), ĭEFINITION 1.2() A binary operation : Ã- is called a continuous t-norm if, (, ) is an abelian topological monoid with unit 1 such that a b c d wheneverĪ c and b d, for all a, b, c, d in. A fuzzy set A in X is a function with domain X and values in. Now,We have used the following notions:ĭEFINITION 1.1() Let X be any set. The aim of this paper is to obtain a common fixed point theorem for compatible pair of self mappings in fuzzy metric space. have proved a fixed point theorems in complete fuzzy metric space by replacing continuity condition with reciprocally continuity maps. As a generalization of fixed point results of Singh and Jain, Mishra et. Jain introduced the notion of semi- compatible mappings in fuzzy metric space and compared this notion with the notion of compatible map of type (), compatible map of type () and obtained some fixed point theorems in complete fuzzy metric space in the sense of Grabiec. have proved a common fixed point theorem for four self maps in fuzzy metric space under the weak contractive conditions. proved a fixed point theorem, which generalizes a result of Pant for fuzzy mappings in fuzzy metric space.Also, Jha et.al. Also, Jungck and Rhoades defined a pair of self mappings to be weakly compatible if they commute at their coincidence points. George and Veeramani have modified the notion of fuzzy metric spaces with the help of continuous t-norm, by generalizing the concept of probabilistic metric space to fuzzy situation. Grabiec proved the contraction principle in the setting of the fuzzy metric space which was further generalization of results by Subrahmanyam for a pair of commuting mappings. Zadeh in 1965 and the concept of fuzzy metric space was introduced by Kramosil and Michalek. The concept of fuzzy sets was initiated by L.A. Key Words and phrases: Common fixed point, Fuzzy metric space, compatible maps. 2000 Mathematics Subject Classification: 54H25, 47H10. Sundarlal Sharma (Open ) University, Chhattisgarh, Bilaspur.Ībstract:- In this research paper we have established a common fixed point theorem for compatible pair of self mappings in a fuzzy metric space. Fixed Point Theorem in Fuzzy Metric Spaceĭeptt.
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