Fixed points for some non-obviously contractive operators
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- by E. De Pascale and L. De Pascale PDF
- Proc. Amer. Math. Soc. 130 (2002), 3249-3254 Request permission
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.References
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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
- Received by editor(s): June 5, 2001
- Published electronically: June 11, 2002
- Communicated by: Jonathan M. Borwein
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3249-3254
- MSC (2000): Primary 47H10, 45D05
- DOI: https://doi.org/10.1090/S0002-9939-02-06704-7
- MathSciNet review: 1913003