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ON FIXED POINTS OF GENERALIZED SET-VALUED CONTRACTIONS

Part of: Connections with other structures, applications Nonlinear operators and their properties

Published online by Cambridge University Press:  23 July 2009

S. BENAHMED  and
D. AZÉ
S. BENAHMED
Affiliation:
ENSET D’Oran, BP 1523 El Ménaouer, 31000 Oran, Algérie (email: sfyabenahmed@yahoo.fr)
D. AZÉ*
Affiliation:
Institut de Mathématiques de Toulouse UMR CNRS 5219, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse cedex 4, France (email: aze@mip.ups-tlse.fr)
*
✉For correspondence; e-mail: aze@mip.ups-tlse.fr
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Abstract

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Using a variational method introduced in [D. Azé and J.-N. Corvellec, ‘A variational method in fixed point results with inwardness conditions’, Proc. Amer. Math. Soc.134(12) (2006), 3577–3583], deriving directly from the Ekeland principle, we give a general result on the existence of a fixed point for a very general class of multifunctions, generalizing the recent results of [Y. Feng and S. Liu, ‘Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings’, J. Math. Anal. Appl.317(1) (2006), 103–112; D. Klim and D. Wardowski, ‘Fixed point theorems for set-valued contractions in complete metric spaces’, J. Math. Anal. Appl.334(1) (2007), 132–139]. Moreover, we give a sharp estimate for the distance to the fixed-points set.

Keywords

complete metric spacesgeneralized set-valued contractionsEkeland’s variational principal

MSC classification

Secondary: 54H25: Fixed-point and coincidence theorems 47H10: Fixed-point theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 1 , February 2010 , pp. 16 - 22
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

References

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