Chidume, C. E.; Zegeye, Habtu; Shahzad, Naseer Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings. (English) Zbl 1106.47054 Fixed Point Theory Appl. 2005, No. 2, 233-241 (2005). There exist many results in the literature regarding the iterative approximation of fixed points or common fixed points in the case of selfmappings, see, for example, the reviewer’s monograph [V. Berinde, “Iterative approximation of fixed points” (Efemeride, Baia Mare) (2002; Zbl 1036.47037)] for a recent survey. In the paper under review, the authors introduce and study a fixed point iterative procedure of Halpern type, constructed by means of the sunny nonexpansive retraction of \(K\), in order to approximate the common fixed points of a family of nonself nonexpansive mappings defined on a nonempty closed convex subset \(K\) of a Banach space satisfying some special geometric properties. Reviewer: Vasile Berinde (Baia Mare) Cited in 29 Documents MSC: 47J25 Iterative procedures involving nonlinear operators 47H10 Fixed-point theorems 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:Banach space; nonexpansive nonself-mapping; common fixed point; convergence theorem Citations:Zbl 1036.47037 PDFBibTeX XMLCite \textit{C. E. Chidume} et al., Fixed Point Theory Appl. 2005, No. 2, 233--241 (2005; Zbl 1106.47054) Full Text: DOI EuDML