TAILIEUCHUNG - báo cáo hóa học: " Convergence and weaker control conditions for hybrid iterative algorithms"

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: Convergence and weaker control conditions for hybrid iterative algorithms | Wang Fixed Point Theory and Applications 2011 2011 3 http content 2011 1 3 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Convergence and weaker control conditions for hybrid iterative algorithms Shuang Wang Correspondence wangshuang19841119@ School of Mathematical Sciences Yancheng Teachers University Yancheng 224051 Jiangsu PR China SpringerOpen0 Abstract Very recently Yao et al. Appl. Math. Comput. 216 822-829 2010 have proposed a hybrid iterative algorithm. Under the parameter sequences satisfying some quite restrictive conditions they derived a strong convergence theorem in a Hilbert space. In this article under the weaker conditions we prove the strong convergence of the sequence generated by their iterative algorithm to a common fixed point of an infinite family of nonexpansive mappings which solves a variational inequality. It is worth pointing out that we use a new method to prove our results. An appropriate example such that all conditions of this result that are satisfied and that other conditions are not satisfied is provided. Furthermore we also give a weak convergence theorem for their iterative algorithm involving an infinite family of nonexpansive mappings in a Hilbert space. MSC 47H05 47H09 47H10 Keywords Strong convergence Variational inequality Fixed points k-Lipschitzian n-strongly monotone Hilbert space 1 Introduction Let H be a real Hilbert space and C be a nonempty closed convex subset of H let F H H be a nonlinear operator. The variational inequality problem is formulated as finding a point x e C such that Fx v - x 0 Vv e C. In 1964 Stampacchia 1 introduced and studied variational inequality initially. It is now well known that variational inequalities cover as diverse disciplines as partial differential equations optimal control optimization mathematical programming mechanics and finance 1-5 . It is known that a mapping T H H is said to be nonexpansive if Tx - .

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