Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:302

Article

Jung, JS

关键词: nonexpansive mapping;    common fixed points;    iteration scheme;    sunny and nonexpansive retraction;   

DOI  :  10.1016/j.jmaa.2004.08.022

来源: Elsevier

【 摘 要 】

The iteration scheme for families of nonexpansive mappings, essentially due to Halpern [Bull. Amer. Math. Soc. 73 (1967) 957-961], is established in a Banach space. The main theorem extends a recent result of O'Hara et al. [Nonlinear Anal. 54 (2003) 1417-1426] to a Banach space setting. For the same iteration scheme, with finitely many mappings, a complementary result to a result of Jung and Kim [Bull. Korean Math. Soc. 34 (1997) 93-102] (also Bauschke [J. Math. Anal. Appl. 202 (1996) 150-159]) is obtained by imposing other condition on the sequence of parameters. Our results also improve results in [C. R. Acad. Sci. Ser A-B Paris 284 (1977) 1357-1359; J. Math. Anal. Appl. 211 (1997) 71-83; Arch. Math. 59 (1992) 486-491] in framework of a Hilbert space. (C) 2004 Elsevier Inc. All rights reserved.

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