Department of Mathematics. Leicester University, Leicester, U.K.
ABSTRACT
It is proved that if S and I are commuting mappings and T and J are commuting mappings of a complete metric space (X,d) into itself satisfying the inequality
d (Sx, Ty) ≤c .max {d(Ix ,Jy), d(Ix,Ty) , d (Sx,J y)}
for all s, y in X, where 0≤ c < 1, if the range of I contains the range of S and the range of J contains the range of T and if l and J are continuous, then S, T, I and J have a unique common fixed point. Other related results are proved.