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: PROJECTION ITERATIVE APPROXIMATIONS FOR A NEW CLASS OF GENERAL RANDOM IMPLICIT QUASI-VARIATIONAL INEQUALITIES | PROJECTION ITERATIVE APPROXIMATIONS FOR A NEW CLASS OF GENERAL RANDOM IMPLICIT QUASI-VARIATIONAL INEQUALITIES HENG-YOU LAN Received 9 November 2005 Accepted 21 January 2006 We introduce a class of projection-contraction methods for solving a class of general random implicit quasi-variational inequalities with random multivalued mappings in Hilbert spaces construct some random iterative algorithms and give some existence theorems of random solutions for this class of general random implicit quasi-variational inequalities. We also discuss the convergence and stability of a new perturbed Ishikawa iterative algorithm for solving a class of generalized random nonlinear implicit quasi-variational inequalities involving random single-valued mappings. The results presented in this paper improve and extend the earlier and recent results. Copyright 2006 Heng-You Lan. 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 Throughout this paper we suppose that R denotes the set of real numbers and Q A p is a complete Ơ-finite measure space. Let E be a separable real Hilbert space endowed with the norm II II and inner product let D be a nonempty subset of E and let CB E denote the family of all nonempty bounded closed subsets of E. We denote by E the class of Borel Ơ-fields in E. In this paper we will consider the following new general random implicit quasi-variational inequality with random multivalued mappings by using a new class of projection method find x Q D and u v J Q E such that g t x t e J t v t u t e T t x t v t e F t x t J t e S t x t and a t u t g t y - g t x t N t f t x t J t g t y - g t x t 0 for all t e Q and g t y e J t v t where g Q X D E f Q X E E and N Q X E X E E are measurable single-valued mappings T S Q X D CB E and F Q X D CB D are random multivalued mappings J Q X D P E is a .
