Another fixed point theorem for nonexpansive potential operators

Biagio Ricceri

Biagio Ricceri

Studia Mathematica, Tome 209 (2012), p. 147-151 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $s u p_{| | x | | = r} J (x) = s u p_{{| | u | |}_{L ² ([0, 1], X)} = r} \int_{0}^{1} J (u (t)) d t$ .

Publié le : 2012-01-01

Zbl 1269.47043

EUDML-ID : urn:eudml:doc:286548

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-2-3,
     author = {Biagio Ricceri},
     title = {Another fixed point theorem for nonexpansive potential operators},
     journal = {Studia Mathematica},
     volume = {209},
     year = {2012},
     pages = {147-151},
     zbl = {1269.47043},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-2-3}
}

Biagio Ricceri. Another fixed point theorem for nonexpansive potential operators. Studia Mathematica, Tome 209 (2012) pp. 147-151. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-2-3/