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
MatematiČki Institut, Knez Mihaila 35, Belgrade 11000, Serbia
Received 3 January 1991; Revised 15 March 1991
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].