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Báo cáo hóa học: " Iterative algorithms for finding a common solution of system of the set of variational inclusion problems and the set of fixed point problems"

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 www.fixedpointtheoryandapplications.eom 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@hotmail.com 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 i.e. 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 .