Set-valued equilibrium problems with applications to Browder variational inclusions and to fixed point theory |
| |
| Institution: | 1. Laboratoire de Mécanique, Physique et Modélisation Mathématique, Université de Médéa, Algeria;2. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;3. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania;1. Key Laboratory of IOT Application Technology of Universities in Yunnan Province, Department of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan 650500, PR China;2. Institute of Plant Nutrition and Natural Resources, Beijing Academy of Agriculture and Forestry Sciences, Beijing 100097, China;1. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;1. Technische Universität Chemnitz, Faculty of Mathematics, Professorship Numerical Mathematics (Partial Differential Equations), 09107 Chemnitz, Germany;2. Technische Universität Dortmund, Faculty of Mathematics, Lehrstuhl LSX, 44227 Dortmund, Germany |
| |
| Abstract: | 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. |
| |
| Keywords: | Set-valued equilibrium problem Set-valued mapping Semicontinuity Variational inclusion Fixed point |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
