Inertial subgradient extragradient methods for solving variational inequality problems and fixed point problems

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Authors

Okeke, Godwin Amechi
Abbas, Mujahid
De la Sen, Manuel

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Publisher

MDPI

Abstract

We propose two new iterative algorithms for solving K-pseudomonotone variational inequality problems in the framework of real Hilbert spaces. These newly proposed methods are obtained by combining the viscosity approximation algorithm, the Picard Mann algorithm and the inertial subgradient extragradient method. We establish some strong convergence theorems for our newly developed methods under certain restriction. Our results extend and improve several recently announced results. Furthermore, we give several numerical experiments to show that our proposed algorithms performs better in comparison with several existing methods.

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Keywords

K-pseudomonotone, Inertial iterative algorithms, Variational inequality problems, Hilbert spaces, Strong convergence

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Citation

Okeke, G.A., Abbas, M. & De la Sen, M. 2020, 'Inertial subgradient extragradient methods for solving variational inequality problems and fixed point problems', Axioms, vol. 9, no. 2, art. 51, pp. 1-24.