Geodesic
An intersection theorem for set-valued mappings
Applications of Mathematics, Tome 58 (2013) no. 3, pp. 269-278.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.1007/s10492-013-0013-7
Classification : 47H04, 47H10, 49J53
Keywords: intersection theorem; fixed point; saddle point; equilibrium problem; complementarity problem 
@article{10_1007_s10492_013_0013_7,
     author = {Agarwal, Ravi P. and Balaj, Mircea and O'Regan, Donal},
     title = {An intersection theorem for set-valued mappings},
     journal = {Applications of Mathematics},
     pages = {269--278},
     publisher = {mathdoc},
     volume = {58},
     number = {3},
     year = {2013},
     doi = {10.1007/s10492-013-0013-7},
     mrnumber = {3066821},
     zbl = {1275.47105},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0013-7/}
}
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
SP  - 269
EP  - 278
VL  - 58
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0013-7/
DO  - 10.1007/s10492-013-0013-7
LA  - en
ID  - 10_1007_s10492_013_0013_7
ER  - 
%0 Journal Article
%A Agarwal, Ravi P.
%A Balaj, Mircea
%A O'Regan, Donal
%T An intersection theorem for set-valued mappings
%J Applications of Mathematics
%D 2013
%P 269-278
%V 58
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0013-7/
%R 10.1007/s10492-013-0013-7
%G en
%F 10_1007_s10492_013_0013_7
Agarwal, Ravi P.; Balaj, Mircea; O'Regan, Donal. An intersection theorem for set-valued mappings. Applications of Mathematics, Tome 58 (2013) no. 3, pp. 269-278. doi : 10.1007/s10492-013-0013-7. http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0013-7/

Cité par Sources :