Mann-type extragradient algorithm for solving variational inequality and fixed point problems

This paper aims to propose a double inertial Mann-type extragradient algorithm using non-monotonic step size and establish a weak convergence result to find a common solution to the variational inequality problem involving pseudo-monotone mapping and fixed point problem for quasi-nonexpansive mapping. Moreover, we establish a strong convergence for the variational inequality involving strongly pseudo-monotone mapping. To illustrate our algorithm’s potential, we present several numerical experiments, including the Nash–Cournot oligopolistic market equilibrium model and fractional programming problem. We also employ performance profiles to discuss the efficiency of our algorithm over earlier established algorithms based on two performance metrics.