International Journal of Mathematics and Mathematical Sciences 
Volume 5 (1982), Issue 1, Pages 203-203
doi:10.1155/S0161171282000192

A generalization of some fixed point theorems of K. M. Ghosh

B. E. Rhoades

 Mathematics Department, Indiana University, Bloomington 47405, Indiana, USA
Received 10 April 1981

Abstract

This note establishes the following result. Let T be a selfmap of a normed linear space E. For 0<λ≤1, define Tλx=λx+(1−λ)Tx for each x in E. If, in addition, S=TTλ satisfies any contractive definition strong enough to guarantee that S has a unique fixed point u in E, and, if TTλu=TλTu, then u is the unique fixed point for T.