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Recessively Compact Sets: Properties and Uses

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Abstract

We develop the concept of recessive compactness recently introduced by Luc and Penot. Then we employ this idea to extend some important results of functional analysis such as closed image criteria, a theorem on a family of unbounded sets having a finite intersection property, an existence condition for a variational inequality problem on a noncompact set, a fixed point theorem for nonexpansive maps on unbounded sets, and an existence result for periodic solutions of a nonlinear differential equation in a Hilbert space without a-priori estimates for the solutions of the equation to stay in a bounded region.

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Authors and Affiliations

  1. Département de Mathématique, Université d'Avignon, 33 Rue Louis Pasteur, 8400, Avignon, France

    Dinh The Luc

  2. Hanoi Institute of Mathematics, Vietnam

    Dinh The Luc

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  1. Dinh The Luc
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The Luc, D. Recessively Compact Sets: Properties and Uses. Set-Valued Analysis 10, 15–35 (2002). https://doi.org/10.1023/A:1014458603461

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  • DOI: https://doi.org/10.1023/A:1014458603461

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