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 Strong Convergence of Monotone Hybrid Method for Maximal Monotone Operators and Hemirelatively Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 261932 14 pages doi 2009 261932 Research Article Strong Convergence of Monotone Hybrid Method for Maximal Monotone Operators and Hemirelatively Nonexpansive Mappings Chakkrid Klin-eam and Suthep Suantai Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200 Thailand Correspondence should be addressed to Suthep Suantai scmti005@ Received 20 May 2009 Accepted 21 September 2009 Recommended by Wataru Takahashi We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Banach space. Copyright 2009 C. Klin-eam and S. Suantai. 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. 1. Introduction Let E be a real Banach space and let E be the dual space of E. Let A be a maximal monotone operator from E to E . It is well known that many problems in nonlinear analysis and optimization can be formulated as follows. Find a point u e E satisfying 0 e Au. We denote by A-10 the set of all points u e C such that 0 e Au. Such a problem contains numerous problems in economics optimization and physics and is connected with a variational inequality problem. It is well known that the variational inequalities are equivalent to the fixed point problems. There are many authors who studied the problem of finding a common element of the fixed point of nonlinear mappings and the set of solutions of a variational inequality in the framework of Hilbert spaces see for .
