We establish the existence and uniqueness results for variational inequality problems on Riemannian manifolds and solve completely the open problem proposed in [21]. Also the relationships between the constrained optimization problem and the variational inequality problems as well as the projections on Riemannian manifolds are studied. Keyword: Variational inequalities; Riemannian manifold; Mon...

We consider a generalized ε-vector equilibrium problem which contain vector equilibrium problems and vector variational inequalities as special cases. By using the KKM theorem,we obtain some existence theorems for the generalized ε-vector equilibrium problem. We also investigate the duality of this generalized ε-vector equilibrium problem and discuss the equivalence relation between solutions o...

Abstract We study a model for fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of velocity symmetric deviatoric stress tensor. This tensor is transported via Zaremba-Jaumann rate, it subject to two dissipation processes: one induced by nonsmooth convex potential diffusion. show short-time existence strong solutions as well their uniqueness class Leray-Hopf...

We show existence and uniqueness of a solution for the non-local vector-valued Allen-Cahn variational inequality in a formulation involving Lagrange multipliers for local and non-local constraints. Furthermore, we propose and analyze a primal-dual active set method for local and non-local vector-valued Allen-Cahn variational inequalities. Convergence of the primal-dual active set algorithm is s...

In this paper, we study the strong convergence of an algorithm to solve variational inequality problem which extends a recent paper (Thong et al., Numerical Algorithms. 78, 1045-1060 (2018)). We reduce and refine some their conditions prove in presence computational errors. Then, using MATLAB software, result will be illustrated with numerical examples. Also, compare our other well-known algori...

* Correspondence: [email protected]. th Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand Abstract In this article, we consider the solutions of the system of generalized variational inequality problems in Banach spaces. By employing the generalized projection operator, the well-known Fan’s KKM theorem and Kakutani-Fan-Glicksberg fixed point theorem, we...