Well-posed equilibrium problems

Monica Bianchi, Rita Pini, G. Kassay, R. Pini

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

In this paper we introduce some notions of well-posedness for scalar equilibrium problems in complete metric spaces or in Banach spaces. As equilibrium problem is a common extension of optimization, saddle point and variational inequality problems, our definitions originates from the well-posedness concepts already introduced for these problems. We give sufficient conditions for two different kinds of well-posedness and show by means of counterexamples that these have no relationship in the general case. However, together with some additional assumptions, we show via Ekeland's principle for bifunctions a link between them. Finally we discuss a parametric form of the equilibrium problem and introduce a well-posedness concept for it, which unifies the two different notions of well-posedness introduced in the first part.
Original languageEnglish
Pages (from-to)460-468
Number of pages9
JournalNONLINEAR ANALYSIS
Volume2010
DOIs
Publication statusPublished - 2010

Keywords

  • approximate solutions
  • equilibrium problems
  • well posedness

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