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  • We prove a variational principle in reflexive Banach spaces X with Kadec-Klee norm, which asserts that any Lipschitz (or any proper lower semicontinuous bounded from below extended real-valued) function in X can be perturbed with a parabola in such a way that the perturbed function attains its infimum (even more can be said - the infimum is well-posed). In addition, we have genericity of the points determining the parabolas. We prove also that the validity of such a principle actually characterizes the reflexive spaces with Kadec-Klee norm. This principle turns out to be an analytic counterpart of a result of K.-S. Lau on nearest points.
  • We prove a variational principle in reflexive Banach spaces X with Kadec-Klee norm, which asserts that any Lipschitz (or any proper lower semicontinuous bounded from below extended real-valued) function in X can be perturbed with a parabola in such a way that the perturbed function attains its infimum (even more can be said - the infimum is well-posed). In addition, we have genericity of the points determining the parabolas. We prove also that the validity of such a principle actually characterizes the reflexive spaces with Kadec-Klee norm. This principle turns out to be an analytic counterpart of a result of K.-S. Lau on nearest points. (en)
Title
  • A Variational Principle in Reflexive Spaces with Kadec-Klee Norm
  • A Variational Principle in Reflexive Spaces with Kadec-Klee Norm (en)
skos:prefLabel
  • A Variational Principle in Reflexive Spaces with Kadec-Klee Norm
  • A Variational Principle in Reflexive Spaces with Kadec-Klee Norm (en)
skos:notation
  • RIV/67985840:_____/09:00337028!RIV10-AV0-67985840
http://linked.open...avai/riv/aktivita
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  • P(GA201/04/0090), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika
  • 1
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  • 301649
http://linked.open...ai/riv/idVysledku
  • RIV/67985840:_____/09:00337028
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  • reflexive space; Kadec-Klee norm; variational principle; perturbed function; well-posed infimum (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [38DA195A5D51]
http://linked.open...i/riv/nazevZdroje
  • Journal of Convex Analysis
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  • 16
http://linked.open...iv/tvurceVysledku
  • Fabian, Marián
  • Revalski, J. P.
http://linked.open...ain/vavai/riv/wos
  • 000268197200011
http://linked.open...n/vavai/riv/zamer
issn
  • 0944-6532
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