Introduction Sessa [9] generalized the notion of commuting maps given by Jungck [2] and introduced weakly commuting mappings. Further, Jungck [3] introduced more generalized commutativity called compatibility. In 1998, Jungck and Rhoades [4] introduced the notion of weakly compatible maps and showed that compatible maps are weakly compatible but converse need not true. Menger [5] introduced the...

in this paper, we give some new definitions of m-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete m-fuzzy metric spaces.

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...