Jung, Jong Soo; Cho, Yeol Je; Agarwal, R. P. Iterative schemes with some control conditions for a family of finite nonexpansive mappings in Banach spaces. (English) Zbl 1109.47056 Fixed Point Theory Appl. 2005, No. 2, 125-135 (2005). The paper presents a strong convergence theorem for an iterative scheme of Halpern type used to approximate common fixed points of a finite family of nonexpansive mappings \(T_1,T_2,\dots,T_n\) which are defined on a uniformly smooth Banach space with a weakly sequentially continuous duality mapping. To obtain the result, it is explicitly assumed that the common fixed point set \(F=\bigcap \limits_{i=1}^{n}F(T_i)\) is nonempty and all circular compositions of \(T_1,T_2,\dots,T_n\) have the same fixed point set \(F\). Reviewer: Vasile Berinde (Baia Mare) Cited in 19 Documents MSC: 47J25 Iterative procedures involving nonlinear operators 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. Keywords:uniformly smooth Banach space; finite family of nonexpansive mappings; fixed point; iterative scheme; strong convergence PDFBibTeX XMLCite \textit{J. S. Jung} et al., Fixed Point Theory Appl. 2005, No. 2, 125--135 (2005; Zbl 1109.47056) Full Text: DOI EuDML