Mann-Type Inertial Accelerated Subgradient Extragradient Algorithm for Minimum-Norm Solution of Split Equilibrium Problems Induced by Fixed Point Problems in Hilbert Spaces

Abstract

This paper presents the Mann-type inertial accelerated subgradient extragradient algorithm with non-monotonic step sizes for solving the split equilibrium and fixed point problems relating to pseudomonotone and Lipschitz-type continuous bifunctions and nonexpansive mappings in the framework of real Hilbert spaces. By sufficient conditions on the control sequences of the parameters of concern, the strong convergence theorem to support the proposed algorithm, which involves neither prior knowledge of the Lipschitz constants of bifunctions nor the operator norm of the bounded linear operator, is demonstrated. Some numerical experiments are performed to show the efficacy of the proposed algorithm.

Keywords

• split equilibrium problems
• split fixed point problems
• pseudomonotone bifunction
• nonexpansive mapping
• subgradient extragradient method
• inertial method