Iterative algorithms for monotone variational inequality and fixed point problems on Hadamard manifolds

Mann-type Tseng’s algorithm and Halpern-type Tseng’s algorithm are shown in this article. They are used to find a common solution from the set of fixed points of nonexpansive mappings and the set of solutions to monotone variational inequality problems in the setting of Hadamard manifolds. We show that any sequence generated by the proposed methods converges to a common solution of the proposed problem. To demonstrate our main convergence theorems, we also provide some numerical examples. Some of the relevant results in the literature have been enhanced and amplified by the results reported in this article.