Approximation of common fixed points of a finite family of Ø - demicontractive mappings by an implicit iteration method.

Abstract

We prove that the Implicit Iteration process of Xu and Ori (2001) converges strongly to the commonfixed pointsof a finite family of Ø - demicontractive mappings in real Hilbertand Banachspaces. Our results extend the results of Osilike (2004a) from strictl pseudocontractive maps to the much more general Ø - demicontractive maps;complement and generalize several others in the literature.

KEY WORDS AND PHRASES: Ø - Demicontractive Maps, Implicit Iteration Process, Fixed Points,Strong Convergence.