An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems |
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| Authors: | Adrian Petru?el Jen-Chih Yao |
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| Institution: | (1) Department of Applied Mathematics, Babeş-Bolyai University Cluj-Napoca, Cluj-Napoca, Romania;(2) Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan |
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| Abstract: | In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive
mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove
a strong convergence theorem for the sequences generated by this new iterative process.
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| Keywords: | Modified extragradient method Viscosity approximation method Fixed point α -inverse-strongly-monotone mapping Nonexpansive mapping Variational inequalities |
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