Strong convergence of a new hybrid algorithm for fixed point problems and equilibrium problems

Abstract

The paper considers the problem of finding a common solution of a pseudomonotone and Lipschitz-type equilibrium problem and a fixed point problem for a quasi nonexpansive mapping in a Hilbert space. A new hybrid algorithm is introduced for approximating a solution of this problem. The presented algorithm can be considered as a combination of the extragradient method (two-step proximal-like method) and a modified version of the normal Mann iteration. It is well known that the normal Mann iteration has the weak convergence, but in this paper we has obtained the strong convergence of the new algorithm under some mild conditions on parameters. Several numerical experiments are reported to illustrate the convergence of the algorithm and also to show the advantages of it over existing methods. First Published Online: 21 Nov 2018

Keywords

• proximal-like method
• extragradient method
• equilibrium problem
• fixed pointproblem