On fixed point approximation method for finite family of $k$-strictly pseudo-contractive mappings and pseudomonotone equilibrium problem in Hadamard space.

In this paper, we first introduce the Halpern iteration process for approximating the solution of the fixed point problem of a finite family of $k$-strictly pseudo-contractive mappings in Hadamard spaces. We also propose an extra gradient Halpern iterative algorithm for approximating a common solution of a finite family of $k_j$-strictly pseudocontractive mappings and a pseudomonotone equilibrium problem in Hadamard space. We prove a strong convergence result without imposing any strict (compactness) conditions for approximating the solutions to the aforementioned problems. We state some consequences of our results and display some numerical examples to show the performance of our results. Our results improve and generalize many recent results in the literature.