Abstract. In this manuscript, we first introduce (α,β)−generalized hybrid mappings in the framework of convex metric spaces, next we show that if S a self-mapping of a nonempty closed convex subset D of a uniformly convex complete metric space (M,ρ,W), then S has at least a fixed point if and only if there is some z in D such that the sequence {Sn(z)}∞ n=1 is bounded, moreover; if D is bounded, then the fixed points set of S is nonempty, closed and convex.
