A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems

Abstract

We introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive method and does not require prior estimate of norm of the bounded linear operator. More so, the cost operator of the variational inequalities does not necessarily needs to satisfies Lipschitz condition. We prove a strong convergence result under some mild conditions and provide an application of our result to split common null point problems. Some numerical experiments are reported to illustrate the performance of the algorithm and compare with some existing methods.

Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems

“…which was first introduced by Giannessi [23]. Recently, several authors have studied and proposed many iterative algorithms for approximating the solutions of variational inequality problem and related optimization problems (see [25,28,29]). The generalized mixed equilibrium problem is very general in the sense that it includes as a special case minimization problems, variational inequality problems, fixed point problems, Nash equilibrium problems in noncooperative games, and many others (see [2,3,7,12,16,18,21,26,[48][49][50]52]).…”