Semicompatibility and fixed point theorems in fuzzy metric space using implicit relation

Semicompatibility and fixed point theorems in fuzzy metric space using implicit relation

Cho et al. [2] introduced the notion of semicompatible maps in a d-topological space. They define a pair of self-maps (S,T) to be semicompatible if conditions (i) Sy = Ty implies that STy = TSy; (ii) for sequence {xn} in X and x ∈ X , whenever {Sxn} → x,{Txn} → x, then STxn → Tx, as n→∞, hold. However, in Fuzzy metric space (ii) implies (i), taking xn = y for all n and x = Ty = Sy. So, we defin...

Semicompatibility and Fixed Point Theorem in Fuzzy Metric Space Using Implicit Function

In this paper we proved fixed point theorem of four mapping on fuzzy metric space based on the concept of semi copatibility using implicit relation. These results generalize several corresponding relations in fuzzy metric space. All the results of this paper are new.

Common Fixed Point Theorems in Fuzzy Metric Space using Implicit Relation

In this paper, we prove common fixed point theorems in fuzzy metric spaces for weakly compatible mappings along with property (E.A.) satisfying implicit relation. Property (E.A.) buys containment of ranges without any continuity requirement besides minimizing the commutativity conditions of the maps to commutativity at their point of coincidence. Moreover, property (E.A.) allows replacing the c...

Semicompatibility and Fixed Point Theorems for Reciprocally Continuous Maps in a Fuzzy Metric Space

Common Fixed Point Theorems on Fuzzy Metric Spaces Using Implicit Relation

Received: 27 March 2012; Accepted: 25 July 2012. Published online: XX July. 2012 Abstract: In this paper, we prove a common fixed point theorem for occasionally weakly compatible mappings on fuzzy metric space satisfying an implicit relation. Our result never requires the completeness (or closedness) of the whole space (or subspaces), containment of ranges amongst involved mappings and continui...