Some iterative methods for finding fixed points and for solving constrained convex minimization problems |
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Authors: | L-C Ceng QH Ansari J-C Yao |
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Institution: | a Department of Mathematics, Shanghai Normal University, Shanghai 200234, Chinab Scientific Computing Key Laboratory of Shanghai Universities, Chinac Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, Indiad Center for General Education, Kaohsiung Medical University, Kaohsiung 80708, Taiwan |
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Abstract: | The present paper is divided into two parts. In the first part, we introduce implicit and explicit iterative schemes for finding the fixed point of a nonexpansive mapping defined on the closed convex subset of a real Hilbert space. We establish results on the strong convergence of the sequences generated by the proposed schemes to a fixed point of a nonexpansive mapping. Such a fixed point is also a solution of a variational inequality defined on the set of fixed points. In the second part, we propose implicit and explicit iterative schemes for finding the approximate minimizer of a constrained convex minimization problem and prove that the sequences generated by our schemes converge strongly to a solution of the constrained convex minimization problem. Such a solution is also a solution of a variational inequality defined over the set of fixed points of a nonexpansive mapping. The results of this paper extend and improve several results presented in the literature in the recent past. |
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Keywords: | Iterative schemes Variational inequality Fixed point Constrained convex minimization Nonexpansive mapping |
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