tailieunhanh - Báo cáo hóa học: "Research Article The Solvability of a Class of General Nonlinear Implicit Variational Inequalities Based on Perturbed Three-Step Iterative Processes with Errors"

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 The Solvability of a Class of General Nonlinear Implicit Variational Inequalities Based on Perturbed Three-Step Iterative Processes with Errors | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 634921 13 pages doi 2008 634921 Research Article The Solvability of a Class of General Nonlinear Implicit Variational Inequalities Based on Perturbed Three-Step Iterative Processes with Errors Zeqing Liu 1 Shin Min Kang 2 and Jeong Sheok Ume3 1 Department of Mathematics Liaoning Normal University . Box 200 Dalian Liaoning 116029 China 2 Department of Mathematics and the Research Institute of Natural Science Gyeongsang National University Jinju 660-701 South Korea 3 Department of Applied Mathematics Changwon National University Changwon 641-733 South Korea Correspondence should be addressed to Shin Min Kang smkang@ Received 23 October 2007 Accepted 25 January 2008 Recommended by Mohammed Khamsi We introduce and study a new class of general nonlinear implicit variational inequalities which includes several classes of variational inequalities and variational inclusions as special cases. By applying the resolvent operator technique and fixed point theorem we suggest a new perturbed three-step iterative algorithm with errors for solving the class of variational inequalities. Several existence and uniqueness results of solutions for the general nonlinear implicit variational inequalities and convergence and stability results of the sequence generated by the algorithm are obtained. The results presented in this paper extend improve and unify a host of results in recent literatures. Copyright 2008 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 In recent years various extensions and generalizations of the variational inequalities have been considered and studied. For details we refer to 1-33 and the references therein. It is well known that one of the most .