New extragradient methods with non-convex combination for pseudomonotone equilibrium problems with application in Hilbert space

Abstract

In the literature, the most authors modify the viscosity methods or hybrid projection methods to construct  the strong convergence algorithms for  solving the pseudomonotone equilibrium problems.   In this paper, we  introduce  some  new extragradient    methods with  non-convex combination    to   solve  the  pseudomonotone equilibrium problems      in Hilbert space  and prove the strong convergence for the constructed    algorithms.  Our algorithms are very different with the existing ones  in the literatures.   As the  application,  the  fixed point theorems  for  strict pseudo-contraction are  considered.   Finally,   some  numerical examples  are given to  show the effectiveness of the algorithms   and compare the computed results with that of others in the literature.