An intersection theorem for set-valued mappings

Agarwal, Ravi P., Balaj, Mircea, and O'Regan, Donal. "An intersection theorem for set-valued mappings." Applications of Mathematics 58.3 (2013): 269-278. <http://eudml.org/doc/252514>.

@article{Agarwal2013,
abstract = {Given a nonempty convex set $X$ in a locally convex Hausdorff topological vector space, a nonempty set $Y$ and two set-valued mappings $T\colon X\rightrightarrows X$, $S\colon Y\rightrightarrows X$ we prove that under suitable conditions one can find an $x\in X$ which is simultaneously a fixed point for $T$ and a common point for the family of values of $S$. Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.},
author = {Agarwal, Ravi P., Balaj, Mircea, O'Regan, Donal},
journal = {Applications of Mathematics},
keywords = {intersection theorem; fixed point; saddle point; equilibrium problem; complementarity problem; intersection theorem; fixed point; saddle point; equilibrium problem; complementarity problem},
language = {eng},
number = {3},
pages = {269-278},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An intersection theorem for set-valued mappings},
url = {http://eudml.org/doc/252514},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Agarwal, Ravi P.
AU - Balaj, Mircea
AU - O'Regan, Donal
TI - An intersection theorem for set-valued mappings
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 3
SP - 269
EP - 278
AB - Given a nonempty convex set $X$ in a locally convex Hausdorff topological vector space, a nonempty set $Y$ and two set-valued mappings $T\colon X\rightrightarrows X$, $S\colon Y\rightrightarrows X$ we prove that under suitable conditions one can find an $x\in X$ which is simultaneously a fixed point for $T$ and a common point for the family of values of $S$. Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.
LA - eng
KW - intersection theorem; fixed point; saddle point; equilibrium problem; complementarity problem; intersection theorem; fixed point; saddle point; equilibrium problem; complementarity problem
UR - http://eudml.org/doc/252514
ER -