<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ABOUBAKARY DIAKHABY</style></author><author><style face="normal" font="default" size="100%">YOUSSEF OUKNINE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HOMOGENIZATION OF BSDES WITH TWO REFLECTING BARRIERS, VARIATIONAL INEQUALITY AND STOCHASTIC GAME</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">58E35</style></keyword><keyword><style  face="normal" font="default" size="100%">60G35</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the limit of semilinear variational inequality with bilateral constraints and stochastic differential games of mixed type. By a penalization method, we first study homogenization properties for system of two barriers reflected backward stochastic differential equation in the Markovian setting. This result together with certain techniques from stochastic calculus is then applied to show that the unique solution of the homogenized problem is also the value function of certain stochastic differential games of mixed type. Then using standard results from the theory of viscosity solutions, we show that the value function of this stochastic differential game with continuous control is the unique viscosity solution of the corresponding limit semilinear variational inequalities too.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">499</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SEHIE PARK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON VARIOUS MULTIMAP CLASSES IN THE KKM THEORY AND THEIR APPLICATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword><keyword><style  face="normal" font="default" size="100%">47J20</style></keyword><keyword><style  face="normal" font="default" size="100%">47N10</style></keyword><keyword><style  face="normal" font="default" size="100%">49J53</style></keyword><keyword><style  face="normal" font="default" size="100%">52A99</style></keyword><keyword><style  face="normal" font="default" size="100%">54C60</style></keyword><keyword><style  face="normal" font="default" size="100%">54H25</style></keyword><keyword><style  face="normal" font="default" size="100%">58E35</style></keyword><keyword><style  face="normal" font="default" size="100%">90C47</style></keyword><keyword><style  face="normal" font="default" size="100%">91A13</style></keyword><keyword><style  face="normal" font="default" size="100%">91B50</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">26</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Fixed point theory of convex-valued multimaps are closely related to the KKM theory from the beginning. In the last twenty-five years, we introduced the acyclic multimap class, the admissible multimap class &lt;em&gt;A&lt;sup&gt;κ&lt;/sup&gt;&lt;sub&gt;c&lt;/sub&gt; &lt;/em&gt;, the better admissible class &lt;em&gt;B&lt;/em&gt;, and the KKM admissible classes &lt;em&gt;KC&lt;/em&gt;, &lt;em&gt;KO&lt;/em&gt; in the frame of the KKM theory. Our aim in this review is to collect the basic properties of our multimap classes and some mutual relations among them in general topological spaces or our abstract convex spaces. We add some new remarks and further comments to improve many of those results, and introduce some recent applications of our multimap classes.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">283</style></section></record></records></xml>