A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in Hadamard spaces

Abstract

In this work, we study a self-adaptive extragradient algorithm for approximating a common solution of a pseudomonotone equilibrium problem and fixed-point problem for multivalued nonexpansive mapping in Hadamard spaces. Our proposed algorithm is designed in such a way that its step size does not require knowledge of the Lipschitz-like constants of the bifunction. Under some appropriate conditions, we establish the strong convergence of the algorithm without prior knowledge of the Lipschitz constants. Furthermore, we provide a numerical experiment to demonstrate the efficiency of our algorithm. This result extends and complements recent results in the literature.