In this paper the regularity of one-parametric optimization problems in the sense of Jongen, Jonker and Twilt is extended to one-parametric variational inequalities. The ve singularities are deened in this context and suitable indices are described around them. Many of the local properties of the singularities are also proved for this case. The generic property of the deened class of regular on...

Various coercivity conditions appear in the literature in order to guarantee solutions for the Variational Inequality Problem. We show that these conditions are equivalent to each other and that they are not only sufficient, but also necessary for the set of solutions to be non-empty and bounded.

In this note we consider a class of environmental games recently proposed in the literature and investigate them by using the powerful tools of variational inequalities. We also consider the case where some data of the problem can depend on a parameter and analyze the regularity of the solution with respect to the parameter. In view of applications to time-dependent or random models, we also in...

‎in a real hilbert space‎, ‎an iterative scheme is considered to‎ ‎obtain strong convergence which is an essential tool to find a‎ ‎common fixed point for a countable family of nonexpansive mappings‎ ‎and the solution of a variational inequality problem governed by a‎ ‎monotone mapping‎. ‎in this paper‎, ‎we give a procedure which results‎ ‎in developing shehu's result to solve equilibrium prob...

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 introduce and study a new class of generalized nonlinear mixed variational-like inequalities in reflexive Banach spaces. By applying Ding’s technique we prove several existence and uniqueness theorems of solutions for the generalized nonlinear mixed variational-like inequality, extend the auxiliary problem technique to suggest and analyze an iterative method to compute the approximate soluti...

We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f -divergences in place of KL divergence, and we assume knowledge of a sequence of values of generalised variational divergences. We then develop a best possible inequality for this doubly generalised situation. Specialising our result to the clas...

This paper proves the equilibrium existence for abstract economies with non-compact infinitedimensional strategy spaces, infinitely many agents, and discontinuous payolT (utility) functions by using the quasi-variational inequality approach. The motivations come from economic applications showing that payoff functions are discontinuous in many cases and the set of feasible allocations generally...

We introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings andmonotone mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of set of fixed points of nonexpansive mapping and the set of solutions of variational inequality for an inversestrongly monotone mappings, whic...