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Báo cáo hóa học: "Research Article Perturbed Iterative Approximation of Solutions for Nonlinear General A-Monotone Operator Equations in Banach Spaces"

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 Perturbed Iterative Approximation of Solutions for Nonlinear General A-Monotone Operator Equations in Banach Spaces | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 290713 13 pages doi 10.1155 2009 290713 Research Article Perturbed Iterative Approximation of Solutions for Nonlinear General A-Monotone Operator Equations in Banach Spaces Xing Wei 1 Heng-you Lan 2 and Xian-jun Zhang2 1 College of Mathematics and Software Science Sichuan Normal University Chengdu Sichuan 610066 China 2 Department of Mathematics Sichuan University of Science Engineering Zigong Sichuan 643000 China Correspondence should be addressed to Heng-you Lan hengyoulan@163.com Received 2 January 2009 Accepted 19 March 2009 Recommended by Ram U. Verma We introduce and study a new class of nonlinear general A-monotone operator equations with multivalued operator. By using Alber s inequalities Nalder s results and the new proximal mapping technique we construct some new perturbed iterative algorithms with mixed errors for solving the nonlinear general A-monotone operator equations and study the approximationsolvability of the nonlinear operator equations in Banach spaces. The results presented in this paper improve and generalize the corresponding results on strongly monotone quasivariational inclusions and nonlinear implicit quasivariational inclusions. Copyright 2009 Xing Wei et al. 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 X be a real Banach space with the topological dual space of X let x y be the pairing between x e X and y e X let2X denote the family of all subsets of X and let CB X denote the family of all nonempty closed bounded subsets of X. We denote by the z x z x for all x e X and z e X . Let f X X T X 2X g X X and A X A X be nonlinear operators and let M X 2X be a general A-monotone operator such that g X dom M - f 0. We will consider the following nonlinear general .