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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 Algorithms for Generalized Nonlinear Set-Valued Quasivariational | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 29863 12 pages doi 10.1155 2007 29863 Research Article Perturbed Iterative Algorithms for Generalized Nonlinear Set-Valued Quasivariational Inclusions Involving Generalized m-Accretive Mappings Mao-Ming Jin Received 24 August 2006 Revised 10 January 2007 Accepted 14 January 2007 Recommended by H. Bevan Thompson A new class of generalized nonlinear set-valued quasivariational inclusions involving generalized m-accretive mappings in Banach spaces are studied which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized m-accretive mappings we established the equivalence between the generalized nonlinear set-valued quasi-variational inclusions and the fixed point problems and some new perturbed iterative algorithms proved that its proximate solution converges strongly to its exact solution in real Banach spaces. Copyright 2007 Mao-Ming Jin. 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 In 1994 Hassouni and Moudafi 1 introduced and studied a class of variational inclusions and developed a perturbed algorithm for finding approximate solutions of the variational inclusions. Since then Adly 2 Ding 3 Ding and Luo 4 Huang 5 6 Huang et al. 7 Ahmad and Ansari 8 have obtained some important extensions of the results in various different assumptions. For more details we refer to 1-29 and the references therein. In 2001 Huang and Fang 16 were the first to introduce the generalized m-accretive mapping and give the definition of the resolvent operator for the generalized m-accretive mappings in Banach spaces. They also showed some properties of the resolvent operator for the generalized m-accretive mappings in Banach .
