Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method |
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| Authors: | Yonghong Yao Yeong-Cheng Liou Shin Min Kang |
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| Affiliation: | 1. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, People’s Republic of China;2. Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan;3. Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea |
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| Abstract: | In this paper, we introduce an iterative method based on the extragradient method for finding a common element of the set of a general system of variational inequalities and the set of fixed points of a strictly pseudocontractive mapping in a real Hilbert space. Furthermore, we prove that the studied iterative method strongly converges to a common element of the set of a general system of variational inequalities and the set of fixed points of a strictly pseudocontractive mapping under some mild conditions imposed on algorithm parameters. |
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