Linear convergence of alternating inertial Tseng-type method for solving inclusion problems on Hadamard manifolds

Abstract The focus of this paper is to introduce an alternating inertial Tseng-type method for approximating singularity point of an inclusion problem which is defined by means of sum of a single-valued vector and a multi-valued vector field in the setting of a Hadamard manifold. Using our iterative method, we prove that the sequence generated by our method converges to a singularity point under some mild conditions. We also establish a linear convergence result when the operator is strongly monotone. As far as we are concerned, there are no results on alternating inertial steps for solving inclusion problems in the settings of Hadamard manifolds. Lastly, we present a numerical example to show the performance of our method. The result present in this article extends and generalizes many related results in the literature.