Approximating fixed points of Suzuki-generalized nonexpansive mappings

Approximating fixed points of Suzuki-generalized nonexpansive mappings

In this paper, we prove weak and strong convergence theorems for Ishikawa iteration of Suzuki-generalized nonexpansive mappings in uniformly convex Banach spaces. Furthermore, we extend the results to CAT(0) spaces. Our work extends the results of Suzuki [T. Suzuki, Fixed point theorems and converge...

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Veröffentlicht in:Nonlinear analysis. Hybrid systems 2011-08, Vol.5 (3), p.583-590
1. Verfasser: Phuengrattana, Withun
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Banach space
CAT spaces
Convergence
Convergence theorem
Fixed point
Fixed points (mathematics)
Hybrid systems
Mapping
Nonexpansive mapping
Nonlinearity
Theorems
Uniformly convex Banach spaces
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Beschreibung
Zusammenfassung:In this paper, we prove weak and strong convergence theorems for Ishikawa iteration of Suzuki-generalized nonexpansive mappings in uniformly convex Banach spaces. Furthermore, we extend the results to CAT(0) spaces. Our work extends the results of Suzuki [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mapping, J. Math. Anal. Appl. 340 (2008) 1088–1095] and Takahashi and Kim [W. Takahashi, G.E. Kim, Approximating fixed points of nonexpansive mappings in Banach spaces, Math. Jpn. 48 (1998) 1–9].
ISSN:1751-570X
DOI:10.1016/j.nahs.2010.12.006