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: Existence of solutions and convergence analysis for a system of quasivariational inclusions in Banach spaces | Chen and Wan Journal of Inequalities and Applications 2011 2011 49 http content 2011 1 49 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Existence of solutions and convergence analysis for a system of quasivariational inclusions in Banach spaces Jia-wei Chen1 2 and Zhongping Wan1 Correspondence . Chen713@ 1School of Mathematics and Statistics Wuhan University Wuhan Hubei 430072 PR China Full list of author information is available at the end of the article Springer Abstract In order to unify some variational inequality problems in this paper a new system of generalized quasivariational inclusion for short SGQVI is introduced. By using Banach contraction principle some existence and uniqueness theorems of solutions for SGQVI are obtained in real Banach spaces. Two new iterative algorithms to find the common element of the solutions set for SGQVI and the fixed points set for Lipschitz mappings are proposed. Convergence theorems of these iterative algorithms are established under suitable conditions. Further convergence rates of the convergence sequences are also proved in real Banach spaces. The main results in this paper extend and improve the corresponding results in the current literature. 2000 MSC 47H04 49J40. Keywords system of generalized quasivariational inclusions problem strong convergence theorem convergence rate resolvent operator relaxed cocoercive mapping 1 Introduction Variational inclusion problems which are generalizations of variational inequalities introduced by Stampacchia 1 in the early sixties are among the most interesting and intensively studied classes of mathematics problems and have wide applications in the fields of optimization and control economics electrical networks game theory engineering science and transportation equilibria. For the past decades many existence results and iterative algorithms for variational inequality and variational .
