Set-Valued Analysis

, Volume 11, Issue 3, pp 225–256

Continuity of Usual Operations and Variational Convergences

  • Jean-Paul Penot
  • Constantin Zălinescu

DOI: 10.1023/A:1024432532388

Cite this article as:
Penot, J. & Zălinescu, C. Set-Valued Analysis (2003) 11: 225. doi:10.1023/A:1024432532388


Given convergent sequences of functions (fn) and (gn), we look for conditions ensuring that the sequences (fn+gn), (max (fn,gn)) and (fn □ gn) converge, □ being the infimal convolution. The convergences we use are variational convergences. This study is motivated by applications to Hamilton–Jacobi equations.

asymptotic functionsbounded-Hausdorff convergencebounded-hemi convergenceconvergenceepiconvergenceHamilton–Jacobi equationsMosco convergencevariational convergence

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Jean-Paul Penot
    • 1
  • Constantin Zălinescu
    • 2
  1. 1.Faculté des sciencesLaboratoire de Mathématiques appliquées, ERS CNRS 2055, av. de l'UniversitéPauFrance
  2. 2.Faculty of MathematicsUniversity “Al. I. Cuza” Iaşi, Bd. Copou Nr. 11IaşiRomania