In this article, we consider an inclusion problem which is defined by means of a sum of a single-valued vector field and a set-valued vector field defined on a Hadamard manifold. We propose Halpern-type and Mann-type algorithms for finding a common point of the set of fixed points of a nonexpansive mapping and the set of solutions of the inclusion problem defined on a Hadamard manifold. Some particular cases of our problem and algorithm are also discussed. We study the convergence of the proposed algorithm to a common point of the set of fixed points of a nonexpansive mapping and the set of solutions of the inclusion problem defined on a Hadamard manifold. As applications of our results and algorithms, we derive the solution methods and their convergence results for the optimization problems, variational inequality problems and equilibrium problems in the setting of Hadamard manifolds.

In this paper, we alter Wang’s new iterative method as well as apply it to find the common solution of fixed point problem (FPP) and split variational inclusion problem ($S_p$VIP) in Hilbert space. We discuss the weak convergence for ($S_p$VIP) and strong convergence for the common solution of ($S_p$VIP) and (FPP) using appropriate assumptions. Some consequences of the proposed methods are studied. We compare our iterative schemes with other existing related schemes.