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Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings. (English) Zbl 1106.47054
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.
MSC:
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
54H25Fixed-point and coincidence theorems in topological spaces