Fixed point theorems under combined topological and variational conditions


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.


Angela Budescu
Department of Mathematics, Babes-Bolyai University,  Cluj-Napoca, Romania

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Fixed point; Critical point; Compact nonlinear operator; Condensing operator; Ekeland’s variational principle.

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A. Budescu, R. Precup, Fixed point theorems under combined topological and variational conditions, Results. Math. 70 (2016) no. 3, 487-497,



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Results in Mathematical

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Springer International Publishing

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