In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces. By means of fixed point theorem, we obtain existence theorem for the system of generalized vector quasi-variational-like inequalities and also derive the existence result of solutions for the generalized vector quasi-variational-like inequalities. Ke...

In the present work, we introduce and study completely generalized quasi-variational inequality problem for fuzzy mappings. By using the definitions of strongly accretive and retraction mappings, we propose an iterative algorithm for computing the approximate solutions of this class of variational inequalities. We prove that approximate solutions obtained by the proposed algorithm converge to t...

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variationallike inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalizedmixed quasi-variational-like inequalities and so on. Bymeans of fixed point the...

In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monot...

In this paper, we first prove a generalization of McClendon’s variational inequality for contractible multimaps. Next, using a new generalized variational inequality, we will prove an existence theorem of Nash equilibrium for the generalized game G = (Xi;Ti, fi)i∈I in a finite dimensional Riemannian manifold. A suitable example for Nash equilibrium is given in a geodesic convex generalized game...

We introduce and study a new system of generalized nonlinear relaxed cocoercive inequality problems and construct an iterative algorithm for approximating the solutions of the system of generalized relaxed cocoercive variational inequalities in Hilbert spaces. We prove the existence of the solutions for the system of generalized relaxed cocoercive variational inequality problems and the converg...

Let C be a nonempty closed and convex subset of a real Hilbert space H. Let Am, Bm : C → H be relaxed cocoercive mappings for each 1 ≤ m ≤ r, where r ≥ 1 is integer. Let f : C → C be a contraction with coefficient k ∈ (0, 1). Let G : C → C be ξ-strongly monotone and L-Lipschitz continuous mappings. Under the assumption ∩m=1GV I(C,Bm, Am) 6= ∅, where GV I(C,Bm, Am) is the solution set of a gener...

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...