Convergence of paths for pseudocontractive mappings in Banach spaces
Authors:
Claudio H. Morales and Jong Soo Jung
Journal:
Proc. Amer. Math. Soc. 128 (2000), 34113419
MSC (1991):
Primary 47H10
Published electronically:
May 18, 2000
MathSciNet review:
1707528
Fulltext PDF Free Access
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Abstract: Let be a real Banach space, let be a closed convex subset of , and let , from into , be a pseudocontractive mapping (i.e. for all and . Suppose the space has a uniformly Gâteaux differentiable norm, such that every closed bounded convex subset of enjoys the Fixed Point Property for nonexpansive selfmappings. Then the path , , defined by the equation is continuous and strongly converges to a fixed point of as , provided that satisfies the weakly inward condition.
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Additional Information
Claudio H. Morales
Affiliation:
Department of Mathematics, University of Alabama, Huntsville, Alabama 35899
Email:
morales@math.uah.edu
Jong Soo Jung
Affiliation:
Department of Mathematics, DongA University, Pusan 604714, Korea
Email:
jungjs@mail.donga.ac.kr
DOI:
http://dx.doi.org/10.1090/S0002993900055738
PII:
S 00029939(00)055738
Keywords:
Pseudocontractive mappings,
uniformly Gâteaux differentiable norm.
Received by editor(s):
September 18, 1998
Received by editor(s) in revised form:
January 22, 1999
Published electronically:
May 18, 2000
Additional Notes:
This paper was carried out while the second author was visiting the University of Alabama in Huntsville under the financial support of the LG Yonam Foundation, 1998, and he would like to thank Professor Claudio H. Morales for his hospitality in the Department of Mathematics.
Communicated by:
David R. Larson
Article copyright:
© Copyright 2000
American Mathematical Society
