Fixed point iteration processes for asymptotically nonexpansive mappings

Authors:
Kok-Keong Tan and Hong Kun Xu

Journal:
Proc. Amer. Math. Soc. **122** (1994), 733-739

MSC:
Primary 47H17; Secondary 47H09, 47H10

DOI:
https://doi.org/10.1090/S0002-9939-1994-1203993-5

MathSciNet review:
1203993

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *X* be a uniformly convex Banach space which satisfies Opial's condition or has a Fréchet differentiable norm, *C* a bounded closed convex subset of *X*, and an asymptotically nonexpansive mapping. It is then shown that the modified Mann and Ishikawa iteration processes defined by and , respectively, converge weakly to a fixed point of *T*.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1203993-5

Keywords:
Fixed point,
asymptotically nonexpansive mapping,
fixed point iteration process,
uniformly convex Banach space,
Fréchet differentiable norm,
Opial's condition

Article copyright:
© Copyright 1994
American Mathematical Society