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Approximation of fixed points of asymptotically nonexpansive mappings

Author: Jürgen Schu
Journal: Proc. Amer. Math. Soc. 112 (1991), 143-151
MSC: Primary 47H10
MathSciNet review: 1039264
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Abstract: Let $ T$ be an asymptotically nonexpansive self-mapping of a non-empty closed, bounded, and starshaped (with respect to zero) subset of a smooth reflexive Banach space possessing a duality mapping that is weakly sequentially continuous at zero. Then, if id-$ T$ is demiclosed and $ T$ satisfies a strengthened regularity condition, the iteration process $ {z_{n + 1}}: = {\mu _{n + 1}}{T^n}({z_n})$ converges strongly to some fixed point of $ T$, provided $ ({\mu _n})$ has certain properties.

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Keywords: Fixed point, iteration process, asymptotically nonexpansive mapping
Article copyright: © Copyright 1991 American Mathematical Society

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