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

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.