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

 

Fixed points for some non-obviously contractive operators


Authors: E. De Pascale and L. De Pascale
Journal: Proc. Amer. Math. Soc. 130 (2002), 3249-3254
MSC (2000): Primary 47H10, 45D05
Published electronically: June 11, 2002
MathSciNet review: 1913003
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Abstract: The use of K-normed spaces gives us the possibility to prove that a fixed point theorem due to B. Luo is equivalent to the Banach Contraction Principle. This confirms the conspiracy among fixed point theorems. Moreover the theorem of Lou is improved and extended to different contexts. A counterexample about the fixed points of the sum of a contraction and an integral operator is given. The usefulness of K-norm is tested on a Volterra integral equation as well.


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Additional Information

E. De Pascale
Affiliation: Dipartimento di Matematica, Universitá della Calabria, 87036 Rende (Cosenza), Italy
Email: e.depascale@unical.it

L. De Pascale
Affiliation: Dipartimento di Matematica Applicata “U.Dini”, Via Bonanno Pisano 25/B, 56126 Pisa, Italy
Email: depascal@dm.unipi.it

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06704-7
PII: S 0002-9939(02)06704-7
Keywords: Fixed points, iterative sequences, K-normed spaces, positive operators, normal cone, contraction operators
Received by editor(s): June 5, 2001
Published electronically: June 11, 2002
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society