Yao, Si-Sheng; Chang, Jin-rong Strong convergence theorems of nonself asymptotically nonexpansive mapping in Banach spaces. (English) Zbl 1221.47134 Math. Sci. Res. J. 15, No. 2, 58-65 (2011). Summary: We obtain the strong convergence of a Halpern type iterative scheme to a fixed point of a non-self asymptotically nonexpansive mapping with respect to a retraction \(P\) in Banach spaces. Our results improve and extend the corresponding results of Jung [6], Song [12,13], and Aoyama [2]. MSC: 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. Keywords:strong convergence; non-self asymptotically nonexpansive mapping; Halpern type iteration scheme PDFBibTeX XMLCite \textit{S.-S. Yao} and \textit{J.-r. Chang}, Math. Sci. Res. J. 15, No. 2, 58--65 (2011; Zbl 1221.47134)