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Strong convergence of path for continuous pseudo-contractive mappings

Author: Claudio H. Morales
Journal: Proc. Amer. Math. Soc. 135 (2007), 2831-2838
MSC (2000): Primary 47H10; Secondary 65J15
Published electronically: February 9, 2007
MathSciNet review: 2317959
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Abstract: The purpose of this paper is to study the convergence of a path that begins at the unique fixed point of a strongly pseudo-contractive operator defined on a closed and convex subset of a reflexive Banach space and converges to a fixed point of a pseudo-contractive mapping. Primarily, it is proven that a convex combination of these two operators is indeed strongly pseudo-contractive under the weakly inward condition. This fact generalizes a result of Barbu for accretive operators.

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Claudio H. Morales
Affiliation: Department of Mathematics, University of Alabama in Huntsville, Huntsville, Alabama 35899

Keywords: Pseudo-contractive operators, weakly inward condition, reflexive Banach spaces, uniformly G\^{a}taux differentiable norm.
Received by editor(s): May 23, 2006
Published electronically: February 9, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society

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