Modified Popov's Extragradient-like Method for Solving a Family of Strongly Pseudomonotone Equilibrium Problems in Real Hilbert Space

In memoriam Professor Charles E. Chidume (1947–2021)

Abstract

In this article, we are introducing a new proximal based extragradient method and examining its convergence analysis in order to solve equilibrium problems that incorporate strongly pseudomonotone bifunction. The main superiority of this technique, in particular that the construction of an approximation solution, proof of its convergence and also proof of its appropriateness, does not needed previous information of the modulus of strong pseudo-monotonicity and the Lipschitz-type bi-functional parameters. In addition, the method uses a decreasing and non-summable stepsize sequence. Finally, numerical experiment results are provided to illustrate the method on a test problem to equate the efficiency with previously known algorithms.