A parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium, fixed point, and split null point problems

Abstract

Abstract This paper provides iterative construction of a common solution associated with the classes of equilibrium problems (EP) and split convex feasibility problems. In particular, we are interested in the EP defined with respect to the pseudomonotone bifunction, the fixed point problem (FPP) for a finite family of -demicontractive operators, and the split null point problem. From the numerical standpoint, combining various classical iterative algorithms to study two or more abstract problems is a fascinating field of research. We, therefore, propose an iterative algorithm that combines the parallel hybrid extragradient algorithm with the inertial extrapolation technique. The analysis of the proposed algorithm comprises theoretical results concerning strong convergence under a suitable set of constraints and numerical results.

Keywords

• Parallel hybrid algorithm
• Inertial extrapolation technique
• Pseudomonotone equilibrium problem
• Fixed point problem
• Null point problem