Journal
FIXED POINT THEORY AND APPLICATIONS
Volume -, Issue -, Pages -Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1186/1687-1812-2013-313
Keywords
extragradient method; CQ method; Mann-type iterative method; viscosity approximation method; variational inequalities; asymptotically strictly pseudocontractive mapping in the intermediate sense; inverse-strong monotonicity
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Funding
- National Science Foundation of China [11071169]
- Innovation Program of Shanghai Municipal Education Commission [09ZZ133]
- Ph.D. Program Foundation of Ministry of Education of China [20123127110002]
- NSC [100-2221-E-182-072-MY2, 99-2115-M-037-002-MY3]
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In the literature, various iterative methods have been proposed for finding a common solution of the classical variational inequality problem and a fixed point problem. Research along these lines is performed either by relaxing the assumptions on the mappings in the settings (for instance, commonly seen assumptions for the mapping involved in the fixed point problem are nonexpansive or strictly pseudocontractive) or by adding a general system of variational inequalities into the settings. In this paper, we consider both possible ways in our settings. Specifically, we propose an iterative method for finding a common solution of the classical variational inequality problem, a general system of variational inequalities and a fixed point problem of a uniformly continuous asymptotically strictly pseudocontractive mapping in the intermediate sense. Our iterative method is hybridized by utilizing the well-known extragradient method, the CQ method, the Mann-type iterative method and the viscosity approximation method. The iterates yielded by our method converge strongly to a common solution of these three problems. In addition, we propose a hybridized extragradient-like method to yield iterates converging weakly to a common solution of these three problems.
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