International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 397-400
doi:10.1155/S016117129300047X
Research notes

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

Ljubomir B. ćirić

MatematiČki Institut, Knez Mihaila 35, Belgrade 11000, Serbia

Received 3 January 1991; Revised 15 March 1991

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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].