Common Fixed Point Theorem in Metric Spaces of Fisher and Sessa

In this paper it is shown that T and I have a unique common fixed point on a compact subset C of a metric space X, where T and I are two self maps on C, I is non-expansive and the pair (T, I) is weakly commuting. In [3] Fisher and Sessa verified the same problem but with C closed subset. Further we show this result by replacing compatibility with weakly commutativity of pair (T, I) and continuity with non-expansiveness of I.