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: Iterative algorithms for finding a common solution of system of the set of variational inclusion problems and the set of fixed point problems | Kangtunyakarn Fixed Point Theory and Applications 2011 2011 38 http content 2011 1 38 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Iterative algorithms for finding a common solution of system of the set of variational inclusion problems and the set of fixed point problems Atid Kangtunyakarn Correspondence beawrock@ Department of Mathematics Faculty of Science King Mongkut s Institute of Technology Ladkrabang Bangkok 10520 Thailand Springer Abstract In this article we introduce a new mapping generated by infinite family of nonexpansive mapping and infinite real numbers. By means of the new mapping we prove a strong convergence theorem for finding a common element of the set of fixed point problems of infinite family of nonexpansive mappings and the set of a finite family of variational inclusion problems in Hilbert space. In the last section we apply our main result to prove a strong convergence theorem for finding a common element of the set of fixed point problems of infinite family of strictly pseudo-contractive mappings and the set of finite family of variational inclusion problems. Keywords nonexpansive mapping strict pseudo contraction strongly positive operator variational inclusion problem fixed point 1 Introduction Let H be a real Hilbert space and let C be a nonempty closed convex subset of H. Let A C H be a nonlinear mapping and let F C X C R be a bifunction. A mapping T of H into itself is called nonexpansive if Tx - Ty x - y for all x y e H. We denote by F T the set of fixed points of T . F T x e H Tx x . Goebel and Kirk 1 showed that F T is always closed convex and also nonempty provided T has a bounded trajectory. The problem for finding a common fixed point of a family of nonexpansive mappings has been studied by many authors. The well-known convex feasibility problem reduces to finding a point in the intersection of the fixed point sets of a family of .
