Strong convergence of path for continuous pseudo-contractive mappings

Morales, Claudio

doi:10.1090/S0002-9939-07-08910-1

Strong convergence of path for continuous pseudo-contractive mappings
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by Claudio H. Morales

Proc. Amer. Math. Soc. 135 (2007), 2831-2838

DOI: https://doi.org/10.1090/S0002-9939-07-08910-1

Published electronically: February 9, 2007

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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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