Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Systems of Generalized Quasivariational Inclusion Problems with Applications in LΓ-Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 561573 12 pages doi 2011 561573 Research Article Systems of Generalized Quasivariational Inclusion Problems with Applications in LT-Spaces Ming-ge Yang 1 2 Jiu-ping Xu 3 and Nan-jing Huang1 3 1 Department of Mathematics Sichuan University Chengdu Sichuan 610064 China 2 Department of Mathematics Luoyang Normal University Luoyang Henan 471022 China 3 College of Business and Management Sichuan University Chengdu Sichuan 610064 China Correspondence should be addressed to Nan-jing Huang nanjinghuang@ Received 27 September 2010 Accepted 22 October 2010 Academic Editor YeolJ. E. Cho Copyright 2011 Ming-ge Yang et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We first prove that the product of a family of Lr-spaces is also an Lr-space. Then by using a Himmelberg type fixed point theorem in Lr-spaces we establish existence theorems of solutions for systems of generalized quasivariational inclusion problems systems of variational equations and systems of generalized quasiequilibrium problems in Lr-spaces. Applications of the existence theorem of solutions for systems of generalized quasiequilibrium problems to optimization problems are given in Lr-spaces. 1. Introduction In 1979 Robinson 1 studied the following parametric variational inclusion problem given x e R find y e Rm such that 0 e g x y Q x yỴ where g R X Rm RF is a single-valued function and Q R X Rm RF is a multivalued map. It is known that covers variational inequality problems and a vast of variational system important in applications. Since then various types of variational inclusion problems have been extended and generalized by many authors see . 2-7 and the references therein . On the other hand Tarafdar 8 generalized the .
