Set-valued equilibrium problems with applications to Browder variational inclusions and to fixed point theory

详细信息    查看全文

• 作者：Boualem Alleche^a ; ^{alleche.boualem@univ-medea.dz" class="auth_mail" title="E-mail the corresponding author} ; ^{alleche.boualem@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Vicenţiu D. Rădulescu^b ; ^c ; ^{vicentiu.radulescu@math.cnrs.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Set-valued equilibrium problem ; Set-valued mapping ; Semicontinuity ; Variational inclusion ; Fixed point
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：28
• 期：Complete
• 页码：251-268
• 全文大小：646 K

文摘

In this paper, we deal with set-valued equilibrium problems under mild conditions of continuity and convexity on subsets recently introduced in the literature. We obtain that neither semicontinuity nor convexity are needed on the whole domain when solving set-valued and single-valued equilibrium problems. As applications, we derive some existence results for Browder variational inclusions, and we extend the well-known Berge maximum theorem in order to obtain two versions of Kakutani and Schauder fixed point theorems.