Abstract. In this paper, we present some fi xed point theorems for fundamentally nonexpansive mappings in Banach spaces and give one common xed point theorem for a commutative family of demiclosed fundamentally nonexpansive mappings on a nonempty weakly compact convex subset of a strictly convex Banach space with the Opial condition and a uniformly convex in every direction Banach space, respectively; moreover, we show that the common fi xed points set of such a family of mappings is closed and convex.
