Fixed points on complete metric spaces;

Uses the property of complete metric space and lemma [1.

Using the property of complete metric space and related lemmas 1 and 2,the existence of common fixed point of a couple of fuzzy contractive mappings with inequality conditions and the cut set being nonempty closed bounded subsets of complete metric space X,is studied;and several theorems on the existence of common fixed point are given.

A new fixed point theorem in complete metric spaces for four mappings;

Fisher B proved the following fixed point theorem:Let (X,d) and (Y,ρ) be complete metric spaces,let T be a continuous mapping of X into Y and let S be a mapping of Y into X satisfying the inequalities  d (STx,STx′)≤C max ｛ d (x,x′), d (x,STx), d (x′,STx′),ρ(Tx,Tx′)｝ρ(TSy,TSy′)≤C max ｛ρ(y,y′),ρ(y,TSy),ρ(y′,TSy′),d(Sy,Sy′)｝ for all x,x′ in X and in Y,where 0≤C<1.

By using the definition for compatible self-mappings in metric spaces,the existence of common fixed point for Φ expansive compatible mappings in complete metric spaces is considered.

On the convergence of the Ishikawa iterates to a common fixed point of two mappings in complete convex metric spaces;

The theorems on Ishikawa ierates strongly converging to a common fixed point for two mappings in complete convex metric spaces;

The existence of common fixed points for commuting mappings in compact metricspaces and complete bounded metric spaces are proved which extend and unify the results ofFisher, Jungck and Leader.