tailieunhanh - Báo cáo hóa học: "Research Article Generalized Strongly Nonlinear Implicit Quasivariational Inequalities"

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 Generalized Strongly Nonlinear Implicit Quasivariational Inequalities | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 124953 16 pages doi 2009 124953 Research Article Generalized Strongly Nonlinear Implicit Quasivariational Inequalities Salahuddin and M. K. Ahmad Department of Mathematics Aligarh Muslim University Aligarh 202002 India Correspondence should be addressed to Salahuddin salahuddin12@ Received 11 February 2009 Accepted 17 June 2009 Recommended by Ram U. Verma We prove an existence theorem for solution of generalized strongly nonlinear implicit quasivaria-tional inequality problems and convergence of iterative sequences with errors involving Lipschitz continuous generalized pseudocontractive and generalized g-pseudocontractive mappings in Hilbert spaces. Copyright 2009 Salahuddin and M. K. Ahmad. 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 Variational inequality was initially studied by Stampacchia 1 in 1964. Since then it has been extensively studied because of its crucial role in the study of mechanics physics economics transportation and engineering sciences and optimization and control. Thanks to its wide applications the classical variational inequality has been well studied and generalized in various directions. For details readers are referred to 2-5 and the references therein. It is known that one of the most important and difficult problems in variational inequality theory is the development of an efficient and implementable approximation schemes for solving various classes of variational inequalities and variational inclusions. Recently Huang 6-8 and Cho et al. 9 constructed some new perturbed iterative algorithms for approximation of solutions of some generalized nonlinear implicit quasi-variational inclusions inequalities which include many iterative algorithms for