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: Composite iterative schemes for maximal monotone operators in reflexive Banach spaces | Cholamjiak et al. Fixed Point Theory and Applications 2011 2011 7 http content 2011 1 7 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Composite iterative schemes for maximal monotone operators in reflexive Banach spaces Prasit Cholamjiak1 Yeol Je Cho2 and Suthep Suantai3 Correspondence yjcho@ scmti005@ department of Mathematics Education and the RINS Gyeongsang NationalUniversity Chinju 660-701 Korea 3Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200 Thailand Full list of author information is available at the end of the article SpringerOpen0 Abstract In this article we introduce composite iterative schemes for finding a zero point of a finite family of maximal monotone operators in a reflexive Banach space. Then we prove strong convergence theorems by using a shrinking projection method. Moreover we also apply our results to a system of convex minimization problems in reflexive Banach spaces. AMS Subject Classification 47H09 47H10 Keywords Maximal monotone operator Shrinking projection method Proximal point algorithm Bregman projection Totally convex function Legendre function Introduction Let E be a real Banach space and C a nonempty subset of E. Let E be the dual space of E. We denote the value of x e E at x 2 E by fx x . Let A E 2E be a setvalued mapping. We denote dom A by domain of A that is dom A x e E Ax 0 and also denote G A by the graph of A that is G A f x x e E X E x e Ax . A set-valued mapping A is said to be monotone if fx - y x - y 0 whenever x x y y e G A . It is said to be maximal monotone if its graph is not contained in the graph of any other monotone operator on E. It is known that if A is maximal monotone then the set A -1 0 z e E 0 e Az is closed and convex. The problem of finding zero points for maximal monotone operators plays an important role in optimizations. This is because it can be reduced to a convex .
