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Zbl 0810.47057
Chidume, C.E.; Osilike, M.O.
Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces. (English)
[J] Numer. Funct. Anal. Optimization 15, No.7-8, 779-790 (1994). ISSN 0163-0563; ISSN 1532-2467/e

Summary: It is proved that the Mann iteration process converges strongly to the fixed point of a strictly hemi-contractive map in real uniformly smooth Banach spaces. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets. A related result deals with the Ishikawa iteration scheme when the mapping is Lipschitzian and strictly hemi-contractive. Our theorems generalize important known results.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47J05 Equations involving nonlinear operators (general)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: Mann iteration process; fixed point of a strictly hemi-contractive map; real uniformly smooth Banach spaces; strictly pseudo-contractive maps with nonempty fixed point sets; Ishikawa iteration scheme; Lipschitzian

Cited in: Zbl 0901.47037

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