Existence theorem and algorithm for a general implicit variational inequality in Banach space |
| |
Authors: | Qing-bang Zhang Ru-liang Deng Liu Liu |
| |
Institution: | aCollege of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, PR China;bDepartment of Mathematics, Sichuan University of Arts and Science, Dazhou, Sichuan 635000, PR China |
| |
Abstract: | By using the generalized f-projection operator, the existence theorem of solutions for the general implicit variational inequality GIVI(T-ξ,K) is proved without assuming the monotonicity of operators in reflexive and smooth Banach space. An iterative algorithm for approximating solution of the general implicit variational inequality is suggested also, and the convergence for this iterative scheme is shown. These theorems extend the corresponding results of Wu and Huang K.Q. Wu, N.J. Huang, Comput. Math. Appl. 54 (2007) 399–406], Wu and Huang K.Q. Wu, N.J. Huang, Bull. Austral. Math. Soc. 73 (2006) 307–317], Zeng and Yao L.C. Zeng, J.C. Yao, J. Optimiz. Theory Appl. 132 (2) (2007) 321–337] and Li J. Li, J. Math. Anal. Appl. 306 (2005) 55–71]. |
| |
Keywords: | General implicit variational inequality Generalized f-projection operator Existence theorem Convergence Banach space |
本文献已被 ScienceDirect 等数据库收录! |
|