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 Auxiliary Principle for Generalized Strongly Nonlinear Mixed Variational-Like Inequalities | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 758786 16 pages doi 2009 758786 Research Article Auxiliary Principle for Generalized Strongly Nonlinear Mixed Variational-Like Inequalities Zeqing Liu 1 Lin Chen 1 Jeong Sheok Ume 2 and Shin Min Kang3 1 Department of Mathematics Liaoning Normal University Dalian Liaoning 116029 China 2 Department of Applied Mathematics Changwon National University Changwon 641-773 South Korea 3 Department of Mathematics Research Institute of Natural Science Gyeongsang National University Jinju 660-701 South Korea Correspondence should be addressed to Jeong Sheok Ume jsume@ Received 4 February 2009 Revised 24 April 2009 Accepted 27 April 2009 Recommended by Nikolaos Papageorgiou We introduce and study a class of generalized strongly nonlinear mixed variational-like inequalities which includes several classes of variational inequalities and variational-like inequalities as special cases. By applying the auxiliary principle technique and KKM theory we suggest an iterative algorithm for solving the generalized strongly nonlinear mixed variational-like inequality. The existence of solutions and convergence of sequence generated by the algorithm for the generalized strongly nonlinear mixed variational-like inequalities are obtained. The results presented in this paper extend and unify some known results. Copyright 2009 Zeqing Liu 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 It is well known that the auxiliary principle technique plays an efficient and important role in variational inequality theory. In 1988 Cohen 1 used the auxiliary principle technique to prove the existence of a unique solution for a variational inequality in reflexive Banach spaces and suggested an innovative and .