An extragradient inertial algorithm for solving split fixed-point problems of demicontractive mappings, with equilibrium and variational inequality problems

Abstract

The purpose of this article is to study and analyse a new extragradient-type algorithm with an inertial extrapolation step for solving split fixed-point problems for demicontractive mapping, equilibrium problem, and pseudomonotone variational inequality problem in real Hilbert spaces. One of the advantages of the proposed algorithm is that a strong convergence result is achieved without a prior estimate of the Lipschitz constant of the cost operator, which is very difficult to find. In addition, the stepsize is generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the Lipschitz constant of the cost operator. Some numerical experiments are reported to show the performance and behaviour of the sequence generated by our algorithm. The obtained results in this article extend and improve many related recent results in this direction in the literature.

Keywords

• variational inequality problem
• pseudomonotone operator
• viscosity iteration
• equilibrium problem
• demicontractive mapping
• split fixed-point
• hilbert space
• 47h09
• 47h10
• 49j20
• 49j40