On Common Fixed Point of a Pair of Contractive Type Mappings -Some Open Problem

Abstract:

      Let S and T be Self-mappings of a Complete metric space (X,d), Suppose ST= TS and for each x∈X, the diameter of the set {T^rS^r′x}_r,r′∈ω is finite. We proveseveral new common fixed point theorems under very general Contractive typecondition of S and r. These theorems improve and extend some main results in thereferences given by us and locally answer some open problem in [1].