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Zbl 1175.47063
Song, Yisheng; Wang, Hongjun
(Song, Yi-sheng; Wang, Hong-jun)
Convergence of iterative algorithms for multivalued mappings in Banach spaces.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 70, No. 4, A, 1547-1556 (2009). ISSN 0362-546X

Summary: We show strong and weak convergence for Mann iteration of multivalued nonexpansive mappings $T$ in a Banach space. Furthermore, we give a strong convergence of the modified Mann iteration which is independent of the convergence of the implicit anchor-like continuous path $z_t \in tu+(1 - t)Tz_t$.
MSC 2000:
*47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47H04 Set-valued operators
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: multivalued nonexpansive mapping; Mann iteration; modified Mann iteration

Cited in: Zbl 1176.47056

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