Extragradient Algorithms with Linesearches for Solving Nonmonotone Equilibrium Problems in Banach Spaces

In this paper, we introduce a new extragradient algorithm with linesearches for solving equilibrium problems in a real Banach space where the bifunction is not required to satisfy any monotone property. Under assumptions on the continuity, convexity of the bifunction, and the nonemptyness of the solution set of the Minty equilibrium problem, we show that the iterative sequences generated by this algorithm converge strongly to a solution to the primal problem. © 2023, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.