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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Continuation method for $\alpha$-sublinear mappings


Author: Yong-Zhuo Chen
Journal: Proc. Amer. Math. Soc. 129 (2001), 203-210
MSC (1991): Primary 47H07, 47H09; Secondary 47H10
Published electronically: August 29, 2000
MathSciNet review: 1694453
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Abstract: Let $B$ be a real Banach space partially ordered by a closed convex cone $P$ with nonempty interior $\overset{\circ}P$. We study the continuation method for the monotone operator $A:\, \overset{\circ}P \rightarrow \overset{\circ}P$ which satisfies

\begin{eqnarraystar}A(tx) \geq t^{\alpha (a,b)}\, A(x), \end{eqnarraystar}



for all $x \in \overset{\circ}P$, $t \in [a,\, b] \subset (0,\, 1)$, where $\alpha (a,b) \in (0,\, 1)$. Thompson's metric is among the main tools we are using.

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Additional Information

Yong-Zhuo Chen
Affiliation: Division of Natural Sciences, University of Pittsburgh at Bradford, Bradford, Pennsylvania 16701
Email: yong@imap.pitt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05514-3
PII: S 0002-9939(00)05514-3
Keywords: $\alpha$-sublinear, cone, fixed point, generalized contraction, monotone operator, ordered Banach space, Thompson's metric
Received by editor(s): September 15, 1997
Received by editor(s) in revised form: April 5, 1999
Published electronically: August 29, 2000
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society