Weak Convergence Theorem of Noor Iterative Scheme for Nonself I-Nonexpansive Mapping

Sukanya Chornphrom, Sirilak Phonin

Abstract

In this paper, we prove the weak convergence of a modified Noor
iteration for nonself I-nonexpansive mapping in a Banach space which satisfies Opial’s condition. Our result extends and improves these announced by Kumam, Kumethog and Jewwaiworn [Weak convergence theorem of Three-step Noor iteration scheme for I-nonexpansive mappings in Banach spaces, Applied Mathematical Science, Vol.2, 2008, no.59, 2915-2920] from self maps into nonself maps. And Kiziltunc and Ozdemir [On convergence theomrem for Nonself I-nonexpansive mapping in Banach spaces, Applied Mathematical Science, Vol.1, 2007, no.48, 2379-2383].