Algorithms of common solutions to quasi variational inclusion and fixed point problems |
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Authors: | Shi-sheng Zhang Joseph H W Lee Chi Kin Chan |
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Institution: | 1. Department of Mathematics, Yibin University, Yibin 644007, Sichuan Province, P. R. China 2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Horn, Kowloon, Hong Kong, P. R. China |
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Abstract: | The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multi-valued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space. Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich (Ekonomika i Matematicheskie Metody, 1976, 12(4):747-756), but also extend and replenish the corresponding results obtained by Iiduka and Takahashi (Nonlinear Anal TMA, 2005, 61(3):341-350), Takahashi and Toyoda (J Optim Theory Appl, 2003,118(2):417-428), Nadezhkina and Takahashi (J Optim Theory Appl, 2006, 128(1):191-201), and Zeng and Yao (Taiwanese Journal of Mathematics, 2006, 10(5):1293-1303). |
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Keywords: | variational inclusion multi-valued maximal monotone mapping inverse-strongly monotone mapping metric projection fixed point nonexpansive mapping |
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