Common Fixed Point for Set and Single Valued Functions without Continuity and Compatibility

Bhavana Deshpande

We prove some common fixed point theorems for set and single valued mappings without assuming continuity and compatibility. We show that completeness of the whole space is not necessary for existence of common fixed point. To prove the theorems we use a new noncompatible condition that is weak commutativity of type (KB). We also prove a fixed point theorem for sequence of set valued mappings.