Dynamical inertial extragradient techniques for solving equilibrium and fixed-point problems in real Hilbert spaces

Abstract

Abstract In this paper, we propose new methods for finding a common solution to pseudomonotone and Lipschitz-type equilibrium problems, as well as a fixed-point problem for demicontractive mapping in real Hilbert spaces. A novel hybrid technique is used to solve this problem. The method shown here is a hybrid of the extragradient method (a two-step proximal method) and a modified Mann-type iteration. Our methods use a simple step-size rule that is generated by specific computations at each iteration. A strong convergence theorem is established without knowing the operator’s Lipschitz constants. The numerical behaviors of the suggested algorithms are described and compared to previously known ones in many numerical experiments.

Keywords

• Equilibrium problem
• Subgradient extragradient method
• Fixed-point problem
• Strong convergence theorems
• Demicontractive mapping