Abstract. We show that for a discrete group G, the equivariant cohomology of a G-space X with G-local coefficients M is isomorphic to the Bredon-Illman cohomology of X with equivariant local coefficients M .

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The aim of this paper is to obtain some new fixed point theorems for single valued mappings and also for hybrid pair of mappings. Our results extend and generalize well known results due to Aamri and El Moutawakil, Sintunavarat and Kumam, Kadelburg et al., and Kamran; and also generalize and rectify some recent results due to Bisht [On Existence of common fixed points under Lipschitz-Type Mapping pairs with Applications, Numer.

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