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Báo cáo hóa học: "Research Article Mixed Variational-Like Inequality for Fuzzy Mappings in Reflexive 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: Research Article Mixed Variational-Like Inequality for Fuzzy Mappings in Reflexive Banach Spaces | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 209485 15 pages doi 10.1155 2009 209485 Research Article Mixed Variational-Like Inequality for Fuzzy Mappings in Reflexive Banach Spaces Poom Kumam1 2 and Narin Petrot2 3 1 Department of Mathematics Faculty of Science King Mongkuts University of Technology Thonburi Bang Mod Bangkok 10140 Thailand 2 Centre of Excellence in Mathematic CHE Sriayudthaya Road Bangkok 10400 Thailand 3 Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Correspondence should be addressed to Narin Petrot narinp@nu.ac.th Received 21 April 2009 Accepted 24 July 2009 Recommended by Vy Khoi Le Some existence theorems for the mixed variational-like inequality for fuzzy mappings FMVLIP in a reflexive Banach space are established. Further the auxiliary principle technique is used to suggest a novel and innovative iterative algorithm for computing the approximate solution. Consequently not only the existence of solutions of the FMVLIP is shown but also the convergence of iterative sequences generated by the algorithm is also proven. The results proved in this paper represent an improvement of previously known results. Copyright 2009 P. Kumam and N. Petrot. 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 The concept of fuzzy set theory was introduced by Zadeh 1 . The applications of the fuzzy set theory can be found in many branches of mathematical and engineering sciences including artificial intelligence control engineering management sciences computer science and operations research 2 . On the other hand the concept of variational inequality was introduced by Hartman and Stampacchia 3 in early 1960s. These have been extended and generalized to study a wide class of problems arising in .