A Self-adaptive Extragradient Method for Fixed Point and Pseudomonotone Equilibrium Problems in Hadamard Spaces

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 a such way that its step-size does not require the knowledge of the Lipschitz-like constants of the bifunction. Under some nice 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 compliments recent results in the literature.