Weerayuth Nilsrakoo
Satit Saejung

A new strong convergence Theorem for non-Lipschitzian Mappings in a uniformly convex Banach Space

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 64, 75 - 86 (2009)

MSC: 47H09   Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
  47H10   Fixed-point theorems
ZDM: -  
CR: -  
PACS: -  

Abstract:   In the present paper, we establish new strong convergence theorems of the modified Mann and the modified Ishikawa iterative scheme with errors for a mapping which is asymptotically nonexpansive in the intermediate sense in a uniformly convex Banach space. Our theorems significantly extend and improve Kim and Kim‘s results. The results in the paper even in the case of asymptotically nonexpansive mappings are new.

Keywords:   asymptotically nonexpansive in the intermediate sense, asymptotically nonexpansive, Mann-type iteration, Ishikawa-type iteration, uniformly convex Banach space
Notes:   The second author was supported by the Commission on Higher Education and the Thailand Research Fund under grant MRG5180146

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