A strong convergence algorithm for approximating a common solution of variational inequality and fixed point problems in real Hilbert space

In this paper, we propose an iterative algorithm for approximating a common solution of a variational inequality and fixed-point problem. The algorithm combines the subgradient extragradient technique, inertial method and a modified viscosity approach. Using this algorithm, we state and prove a strong convergence algorithm for obtaining a common solution of a pseudomonotone variational inequality problem and fixed-point of an η-demimetric mapping in a real Hilbert space. We give an application of this result to some theoretical optimization problems. Furthermore, we report some numerical examples to show the efficiency of our method by comparing it with previous methods in the literature. Our result extends, improves and unifies many other results in this direction in the literature. Mathematics Subject Classification (2010): 47H09, 49J35, 90C47. Received 21 May 2021; Accepted 14 July 2021