Strong convergence theorems by hybrid methods for a finite family of nonexpansive mappings and inverse-strongly monotone mappings |
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Authors: | Sornsak Thianwan |
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Institution: | aSchool of Science and Technology, Naresuan Phayao University, Phayao, 56000, Thailand |
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Abstract: | In this paper, we introduce and study an iterative scheme by a hybrid method for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a real Hilbert space. Then, we prove that the iterative sequence converges strongly to a common element of the three sets. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area. |
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Keywords: | Equilibrium problem Variational inequality Nonexpansive mapping Strong convergence Hybrid method |
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