Fixed Point Theorems for Asymptotically Contractive Multimappings

In this paper, we investigate fixed point theorems for nonexpansive multifunctions relations, multimaps, set-valued mappings, or correspondences satisfying some asymptotic condition. This study has been the subject of numerous works 1–6 for an asymptotically contractive mapping. Our aim here is to obtain some generalization by using the notion of semiasymptotically contractive multimappings which is introduced below. For doing so, we need to fix some notations and conventions. Given a normed vector space n.v.s. X, ‖·‖ , the open ball with center x and radius r in X is denoted by B x, r ; the closed, unit ball is denoted by BX . For any subsets C, D ⊂ X, we set