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Báo cáo hóa học: "ITERATIVE ALGORITHM FOR SOLVING MIXED QUASI-VARIATIONAL-LIKE INEQUALITIES WITH SKEW-SYMMETRIC TERMS IN BANACH SPACES"

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: ITERATIVE ALGORITHM FOR SOLVING MIXED QUASI-VARIATIONAL-LIKE INEQUALITIES WITH SKEW-SYMMETRIC TERMS IN BANACH SPACES | ITERATIVE ALGORITHM FOR SOLVING MIXED QUASI-VARIATIONAL-LIKE INEQUALITIES WITH SKEW-SYMMETRIC TERMS IN bAnACH spaces LU-CHUAN CENG QAMRUL HASAN ANSARI AND JEN-CHIH YAO Received 1 April 2006 Accepted 28 May 2006 We develop an iterative algorithm for computing the approximate solutions of mixed quasi-variational-like inequality problems with skew-symmetric terms in the setting of reflexive Banach spaces. We use Fan-KKM lemma and concept of n-cocoercivity of a composition mapping to prove the existence and convergence of approximate solutions to the exact solution of mixed quasi-variational-like inequalities with skew-symmetric terms. Furthermore we derive the posteriori error estimates for approximate solutions under quite mild conditions. Copyright 2006 Lu-Chuan Ceng 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 variational inequality theory as a very effective and powerful tool not only has stimulated new results dealing with partial differential equations but also has been applied to a large variety of problems arising in mechanics contact problems in elasticity optimization and control problems management science operations research general equilibrium problems in economics and transportation unilateral problems obstacle problems and so forth. Because of its wide applications the classical variational inequality has been studied and generalized in various directions previously by many authors. Among these generalizations mixed variational-like inequality problem is of interest and importance. One of the most important and interesting problems in the theory of variational inequality is the development of an efficient and implementable algorithm for solving variational inequality and its generalizations. These methods include projection method and its variant