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ISSN 1088-6826(e) ISSN 0002-9939(p)

Global iteration schemes for strongly pseudo-contractive maps

Author(s): C. E. Chidume
Journal: Proc. Amer. Math. Soc. 126 (1998), 2641-2649.
MSC (1991): Primary Primnary, 47H17, 47H06, 47H15
MathSciNet review: 1451791
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Abstract: Suppose is a real uniformly smooth Banach space, is a nonempty closed convex and bounded subset of , and $T:K\to K$ is a strong pseudo-contraction. It is proved that if has a fixed point in then both the Mann and the Ishikawa iteration processes, for an arbitrary initial vector in , converge strongly to the unique fixed . 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.

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