In this paper we have established some fixed point theorems in complete and compact metric spaces.

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The notion of compatibility for point-to-point mappings recently defined by Jungck is generalized to include multi-valued mappings. This idea is used to establish a fixed point theorem for a generalized contractive multi-valued mapping and a single-valued napping.

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ABSTRACT. We censider two selfmaps T and of a closed convex subset C of a Bar.ach space X which are weakly commuting in X, i.e.