Abstract
The new idea is to replace part of the conditions on the operator involved in the classical fixed point theorems of Schauder, Krasnoselskii, Darbo and Sadovskii, by assumptions upon the associated functional, in case that the fixed point equation has a variational form. Fixed points minimizing the associated functionals are obtained via Ekeland’s variational principle and the Palais–Smale compactness condition guaranteed by the topological properties of the nonlinear operators.
Authors
Angela Budescu
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Fixed point; Critical point; Compact nonlinear operator; Condensing operator; Ekeland’s variational principle.
Paper coordinates
A. Budescu, R. Precup, Fixed point theorems under combined topological and variational conditions, Results. Math. 70 (2016) no. 3, 487-497, https://doi.org/10.1007/s00025-016-0589-9
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About this paper
Journal
Results in Mathematical
Publisher Name
Springer International Publishing
Print ISSN
422-6383
Online ISSN
1420-9012
google scholar link
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