Geodesic
Another fixed point theorem for nonexpansive potential operators
Biagio Ricceri1
1 Department of Mathematics University of Catania Viale A. Doria 6 95125 Catania, Italy
Studia Mathematica, Tome 211 (2012) no. 2, pp. 147-151

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove the following result: Let $X$ be a real Hilbert space and let $J:X\to \mathbb{R}$ be a $C^1$ 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 $$ \sup_{\|x\|=r}J(x)=\sup_{\|u\|_{L^2([0,1],X)}=r} \,\int_0^1J(u(t))\,dt. $$
DOI : 10.4064/sm211-2-3
Keywords: prove following result real hilbert space mathbb functional nonexpansive derivative each following alternative holds either has fixed point norm nbsp sup sup int

Biagio Ricceri 1

1 Department of Mathematics University of Catania Viale A. Doria 6 95125 Catania, Italy 
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Biagio Ricceri. Another fixed point theorem for nonexpansive potential operators. Studia Mathematica, Tome 211 (2012) no. 2, pp. 147-151. doi: 10.4064/sm211-2-3

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