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: Review Article Super-Relaxed (η)-Proximal Point Algorithms, Relaxed (η)-Proximal Point Algorithms, Linear Convergence Analysis, and Nonlinear Variational Inclusions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 957407 47 pages doi 2009 957407 Review Article Super-Relaxed n -Proximal Point Algorithms Relaxed n -Proximal Point Algorithms Linear Convergence Analysis and Nonlinear Variational Inclusions Ravi P. Agarwal1 2 and Ram U. Verma1 3 1 Department of Mathematical Sciences Florida Institute of Technology Melbourne FL 32901 USA 2 Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia 3 International Publications USA 12085 Lake Cypress Circle Suite I109 Orlando FL 32828 USA Correspondence should be addressed to Ravi P. Agarwal agarwal@ Received 26 June 2009 Accepted 30 August 2009 Recommended by Lai Jiu Lin We glance at recent advances to the general theory of maximal set-valued monotone mappings and their role demonstrated to examine the convex programming and closely related field of nonlinear variational inequalities. We focus mostly on applications of the super-relaxed n -proximal point algorithm to the context of solving a class of nonlinear variational inclusion problems based on the notion of maximal n -monotonicity. Investigations highlighted in this communication are greatly influenced by the celebrated work of Rockafellar 1976 while others have played a significant part as well in generalizing the proximal point algorithm considered by Rockafellar 1976 to the case of the relaxed proximal point algorithm by Eckstein and Bertsekas 1992 . Even for the linear convergence analysis for the overrelaxed or super-relaxed n -proximal point algorithm the fundamental model for Rockafellar s case does the job. Furthermore we attempt to explore possibilities of generalizing the Yosida regularization approximation in light of maximal n -monotonicity and then applying to first-order evolution equations inclusions. Copyright 2009 R. P. Agarwal and R. U. Verma. This is an open access article distributed under the .
