tailieunhanh - Báo cáo hóa học: " Research Article A System of Random Nonlinear Variational Inclusions Involving Random Fuzzy Mappings "

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 A System of Random Nonlinear Variational Inclusions Involving Random Fuzzy Mappings | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 123524 17 pages doi 2010 123524 Research Article A System of Random Nonlinear Variational Inclusions Involving Random Fuzzy Mappings and H -Monotone Set-Valued Mappings Xin-kun Wu and Yun-zhi Zou College of Mathematics Sichuan University Chengdu Sichuan 610064 China Correspondence should be addressed to Yun-zhi Zou zouyz@ Received 8 June 2010 Accepted 24 July 2010 Academic Editor Qamrul Hasan Ansari Copyright 2010 . Wu and . Zou. 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. We introduce and study a new system of random nonlinear generalized variational inclusions involving random fuzzy mappings and set-valued mappings with H - -monotonicity in two Hilbert spaces and develop a new algorithm which produces four random iterative sequences. We also discuss the existence of the random solutions to this new kind of system of variational inclusions and the convergence of the random iterative sequences generated by the algorithm. 1. Introduction The classic variational inequality problem VI F K is to determine a vector x e K c Rn such that F x T x - x ỳ 0 Yx e K where F is a given continuous function from K to Rn and K is a given closed convex subset of the n-dimensional Euclidean space Rn. This is equivalent to find an x e K such that 0 e F x f Ni x f where N1 is normal cone operator. Due to its enormous applications in solving problems arising from the fields of economics mechanics physical equilibrium analysis optimization and control transportation 2 Journal of Inequalities and Applications equilibrium and linear or nonlinear programming etcetera variational inequality and its generalizations have been extensively studied during the past 40 years. For details we refer readers to