Another fixed point theorem for nonexpansive potential operators

Biagio Ricceri. "Another fixed point theorem for nonexpansive potential operators." Studia Mathematica 211.2 (2012): 147-151. <http://eudml.org/doc/286548>.

@article{BiagioRicceri2012,
abstract = {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 $sup_\{||x||=r\}J(x) = sup_\{||u||_\{L²([0,1],X)\}=r\} ∫_\{0\}^\{1\} J(u(t))dt$.},
author = {Biagio Ricceri},
journal = {Studia Mathematica},
keywords = {fixed point; nonexpansive potential operator; Jensen inequality},
language = {eng},
number = {2},
pages = {147-151},
title = {Another fixed point theorem for nonexpansive potential operators},
url = {http://eudml.org/doc/286548},
volume = {211},
year = {2012},
}

TY - JOUR
AU - Biagio Ricceri
TI - Another fixed point theorem for nonexpansive potential operators
JO - Studia Mathematica
PY - 2012
VL - 211
IS - 2
SP - 147
EP - 151
AB - 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 $sup_{||x||=r}J(x) = sup_{||u||_{L²([0,1],X)}=r} ∫_{0}^{1} J(u(t))dt$.
LA - eng
KW - fixed point; nonexpansive potential operator; Jensen inequality
UR - http://eudml.org/doc/286548
ER -