Set-Valued Analysis

, Volume 10, Issue 1, pp 15–35 | Cite as

Recessively Compact Sets: Properties and Uses

  • Dinh The Luc


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.

recessively compact set variational inequality closed image finite intersection property fixed point theorem periodic solution of a differential equation 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Dinh The Luc
    • 1
    • 2
  1. 1.Département de MathématiqueUniversité d'AvignonAvignonFrance
  2. 2.Hanoi Institute of MathematicsVietnam

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