Global iteration schemes for strongly pseudo-contractive maps
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Abstract:
Suppose $E$ is a real uniformly smooth Banach space, $K$ is a nonempty closed convex and bounded subset of $E$, and $T:K\to K$ is a strong pseudo-contraction. It is proved that if $T$ has a fixed point in $K$ then both the Mann and the Ishikawa iteration processes, for an arbitrary initial vector in $K$, converge strongly to the unique fixed $T$. No continuity assumption is necessary for this convergence. Moreover, our iteration parameters are independent of the geometry of the underlying Banach space and of any property of the operator.References
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Additional Information
- C. E. Chidume
- Affiliation: International Centre for Theoretical Physics, 34100 Trieste, Italy
- MR Author ID: 232629
- Email: chidume@ictp.trieste.it
- Received by editor(s): April 22, 1996
- Received by editor(s) in revised form: January 27, 1997
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2641-2649
- MSC (1991): Primary Primnary, 47H17, 47H06, 47H15
- DOI: https://doi.org/10.1090/S0002-9939-98-04322-6
- MathSciNet review: 1451791