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Strong convergence of path for continuous pseudo-contractive mappings
Author(s):
Claudio
H.
Morales
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2831-2838.
MSC (2000):
Primary 47H10;
Secondary 65J15
Posted:
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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Additional Information:
Claudio
H.
Morales
Affiliation:
Department of Mathematics, University of Alabama in Huntsville, Huntsville, Alabama 35899
Email:
morales@math.uah.edu
DOI:
10.1090/S0002-9939-07-08910-1
PII:
S 0002-9939(07)08910-1
Keywords:
Pseudo-contractive operators,
weakly inward condition,
reflexive Banach spaces,
uniformly G\^{a}taux differentiable norm.
Received by editor(s):
May 23, 2006
Posted:
February 9, 2007
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
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