COMMON FIXED POINTS OF THREE-STEP ITERATIONS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN BANACH SPACES

Utith Inprasit (Thailand) and Hathaikarn Wattanataweekul (Thailand)

Received March 20, 2009

Abstract

In this paper, we define a new three-step iterative scheme for three asymptotically nonexpansive mappings in a uniformly convex Banach space. The iteration generalizes the modified Noor iteration defined by S. Suantai and the three-step mean value iterative scheme defined by W. Nilsrakoo and S. Saejung. Strong and weak convergence to a common fixed point of the three mappings of the iteration are established. Our results extend and improve the recent ones announced by Suantai [16], Xu and Noor [20], Mann [6], Ishikawa [4] and many others.

Keywords and phrases: common fixed point, fixed point iteration, three-step iteration, asymptotically nonexpansive mapping, uniformly convex, strongly convergence, weakly convergence.