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Fixed point theorems under the interior condition
Authors:
Antonio Jiménez-Melado and Claudio H. Morales
Journal:
Proc. Amer. Math. Soc. 134 (2006), 501-507
MSC (2000):
Primary 47H10, 47H09
Posted:
July 8, 2005
MathSciNet review:
2176019
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Abstract: We show a fixed point theorem for condensing mappings under a new condition of the Leray-Schauder type. We call it the Interior Condition. We also discuss examples that demonstrate the independence of these two conditions.
References
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B. N. SADOVSKII, On a fixed point principle, Funktsional. Anal. i Prilozhen. 1(2) (1967), 74-76. MR 0211302 (35:2184)
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Additional Information
Antonio Jiménez-Melado
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, University of Málaga, 29071 Málaga, Spain
Email:
melado@uma.es
Claudio H. Morales
Affiliation:
Department of Mathematics, University of Alabama in Huntsville, Huntsville, Alabama 35899
Email:
morales@math.uah.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08021-4
PII:
S 0002-9939(05)08021-4
Keywords:
Condensing mappings,
nonexpansive mappings,
Leray-Schauder condition,
interior condition,
Banach spaces
Received by editor(s):
June 23, 2004
Received by editor(s) in revised form:
September 27, 2004
Posted:
July 8, 2005
Additional Notes:
This research was partially supported by a Grant from Ministerio de Educación y Ciencia, Spain (MTN 2004-00078), and from La Junta de Andalucía (FQM210)
Communicated by:
Joseph A. Ball
Article copyright:
© Copyright 2005 American Mathematical Society
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