Strong convergence of the tseng extragradient method for solving variational inequalities

In this paper, we propose a new iterative algorithm for finding a common element of the set of solutions of the variational inequality problem involving monotone operators and the set of fixed points problems involving quasi-nonexpansive mappings with a demiclosedness property in a Hilbert space. We combine Tseng extragradient method with the Mann approximation method and Yamada’s algorithm. The main advantages of our algorithm are that the construction of solutions and the knowledge of the Lipschitz constant of the operators does not require to be known. We proved that the sequence generated by the new algorithm is strongly convergent. Finally, we provide a numerical example to show the effectiveness of the proposed algorithm. ©2020 Applied Set-Valued Analysis and Optimization