An inertial Mann algorithm for nonexpansive mappings on Hadamard manifolds

An inertial Mann algorithm will be presented in this article with the purpose of approximating a fixed point of a nonexpansive mapping on a Hadamard manifold. Any sequence that is generated by using the proposed approach, under suitable assumptions, converges to fixed points of nonexpansive mappings. The proposed method is also dedicated to solving inclusion and equilibrium problems. Lastly, we give a number of computational experiments that show how well the inertial Mann algorithm works and how it compares to other methods.

Automated summary

An inertial Mann algorithm is presented in this article to approximate fixed points of nonexpansive mappings on a Hadamard manifold. Any sequence generated by this method converges to fixed points of nonexpansive mappings under suitable assumptions. In addition, the proposed algorithm is capable of solving inclusion and equilibrium problems. Computational experiments are conducted to demonstrate the effectiveness of the inertial Mann algorithm and its comparison to other methods.