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Volume :8 Issue : 1 1981      Add To Cart                                                                    Download

Four mappings with a common fixed point

Auther : BRIAN FISHER

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.

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