The work of this author is based on the research supported supported wholly by the National Research Foundation (NRF) of South Africa (Grant Numbers: 111992). Opinions expressed and conclusions arrived at, are those of the authors and are not necessarily to be attributed to the NRF. Y. Shehu: The research of this author is supported by the Alexander von Humboldt-Foundation.
This paper studies an iterative method with inertial term extrapolation step for solving an equilibrium problem of nonmonotone bifunctions in real Hilbert spaces. The inertia term extrapolation step is introduced to speed up the rate of convergence of the iteration process. We obtain convergence result under some continuity and convexity assumptions on the bifunction and the condition that the solution set of the associated Minty equilibrium problem is nonempty. Numerical comparisons of our proposed method with some other related method in the literature are given.