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Báo cáo hóa học: "CONVERGENCE AND STABILITY OF A THREE-STEP ITERATIVE ALGORITHM FOR A GENERAL QUASI-VARIATIONAL INEQUALITY PROBLEM"

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: CONVERGENCE AND STABILITY OF A THREE-STEP ITERATIVE ALGORITHM FOR A GENERAL QUASI-VARIATIONAL INEQUALITY PROBLEM | CONVERGENCE AND STABILITY OF A THREE-STEP ITERATIVE ALGORITHM FOR A GENERAL QUASI-VARIATIONAL INEQUALITY PROBLEM K. R. KAZMI AND M. I. BHAT Received 11 February 2005 Revised 10 September 2005 Accepted 13 September 2005 We consider a general quasi-variational inequality problem involving nonlinear non-convex and nondifferentiable term in uniformly smooth Banach space. Using retraction mapping and fixed point method we study the existence of solution of general quasi-variational inequality problem and discuss the convergence analysis and stability of a three-step iterative algorithm for general quasi-variational inequality problem. The theorems presented in this paper generalize improve and unify many previously known results in the literature. Copyright 2006 K. R. Kazmi and M. I. Bhat. 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 Many problems arising in physics mechanics elasticity and engineering sciences can be formulated in variational inequalities involving nonlinear nonconvex and nondifferen-tiable term see for example Baiocchi and Capelo 4 Duvaut and Lions 8 and Kikuchi and Oden 15 . The proximal resolvent method used to study the convergence analysis of iterative algorithms for variational inclusions see 14 20 cannot be adopted for studying such classes of variational inequalities due to the presence of nondifferentiable term. There are some methods for example projection method and auxiliary principle method which can be used to study such classes of variational inequalities see 7 1719 and the relevent references cited therein. It is remarked that most of the work using projection method and auxiliary principle method has been done in the setting of Hilbert space. Recently Alber and Yao 3 and Chen et al. 6 studied some classes of covariational inequality and co-complementarity .