Bi-step Method for Variational Inequalities on Riemannian Manifold of Non-negative Constant Curvature

In this paper, we have proposed a bi-step method for solving variational inequalities on Riemannian manifold with the use of auxiliary principle technique. A relaxed condition of monotonicity has been used to show the convergence of this newly defined method. Furthermore, several important characterizations for the convex functions on the strongly convex subset of Riemannian manifold have also been discussed.