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In this paper, we are concerned with the problem of finding fixed points of nonexpansive mappings on Hadamard manifolds. To solving this kind of problem, a modified Riemannian Halpern algorithm, which is a natural generalization of a modified Halpern algorithm in Euclidean space is proposed. By giving some mild assumptions and necessary lemmas, the global convergence of the proposed algorithm is established. Finally, when the problem is solved in the framework of Hadamard manifolds, the numerical experiments show the effectiveness of the proposed algorithm, especially in computational time and number of iterations.

A modified Riemannian Halpern algorithm for nonexpansive mappings on Hadamard manifolds