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A general implicit iteration for finding fixed points of nonexpansive mappings. (English) Zbl 1381.47062
Summary: The aim of the paper is to construct an iterative method for finding the fixed points of nonexpansive mappings. We introduce a general implicit iterative scheme for finding an element of the set of fixed points of a nonexpansive mapping defined on a nonempty closed convex subset of a real Hilbert space. A strong convergence theorem for the proposed iterative scheme is proved under certain assumptions imposed on the sequence of parameters. Our results extend and improve the results given by Y. Ke and C. Ma [Fixed Point Theory Appl. 2015, Paper No. 190, 21 p. (2015; Zbl 1346.47047)], H.-K. Xu et al. [ibid. 2015, Paper No. 41, 12 p. (2015; Zbl 1310.47106)], and many others.
MSC:
 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
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