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Hybrid iteration method for fixed points of nonexpansive mappings in arbitrary Banach spaces. (English) Zbl 1156.47311

Summary: We prove that recent results of L.Wang [Fixed Point Theory Appl.2007, Article ID 28619(2007; Zbl 1159.47052)] concerning the iterative approximation of fixed points of nonexpansive mappings using a hybrid iteration method in Hilbert spaces can be extended to arbitrary Banach spaces without the strong monotonicity assumption imposed on the hybrid operator.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Citations:

Zbl 1159.47052
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References:

[1] Wang L: An iteration method for nonexpansive mappings in Hilbert spaces.Fixed Point Theory and Applications 2007, 2007: 8 pages. · Zbl 1159.47052 · doi:10.1155/2007/28619
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[3] Yamada, I.; Butnariu, D. (ed.); Censor, Y. (ed.); Reich, S. (ed.), The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings, No. 8, 473-504 (2001), Amsterdam, The Netherlands · Zbl 1013.49005 · doi:10.1016/S1570-579X(01)80028-8
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[7] Osilike MO, Aniagbosor SC, Akuchu BG: Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces.Panamerican Mathematical Journal 2002,12(2):77-88. · Zbl 1018.47047
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