A remark on Rhoades fixed point theorem for non‐self mappings

Let X be a Banach space, K a non-empty closed subset of X and T:K→X a mapping satisfying the contractive definition (1.1) below and the condition T(∂K)⫅K . Then T has a unique fixed point in K . This result improves Theorem of Rhoades [1] and generalizes the corresponding theorem of Assad [2].