Another fixed point theorem for nonexpansive potential operators

• Autorzy: Biagio Ricceri
• Języki publikacji: EN

Abstrakty

EN

We prove the following result: Let X be a real Hilbert space and let J: X → ℝ be a C¹ functional with a nonexpansive derivative. Then, for each r > 0, the following alternative holds: either J' has a fixed point with norm less than r, or
$sup_{||x||=r}J(x) = sup_{||u||_{L²([0,1],X)}=r} ∫_{0}^{1} J(u(t))dt$.

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 47H10: Fixed-point theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 211
• Numer: 2
• Strony: 147-151

Daty

wydano

2012

Twórcy

autor

Biagio Ricceri

• Department of Mathematics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy

Identyfikatory

DOI

10.4064/sm211-2-3