In this paper, we introduce an iterative sequence by using a hybrid generalized f−projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping and the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational ...

We consider a vector variational inequality in a finite-dimensional space. A new gap function is proposed, and an equivalent optimization problem for the vector variational inequality is also provided. Under some suitable conditions, we prove that the gap function is directionally differentiable and that any point satisfying the first-order necessary optimality condition for the equivalent opti...

A new generalized nonlinear variational-like inequality is introduced and studied. By applying the auxiliary principle technique and KKM theory, we construct a new iterative algorithm for solving the generalized nonlinear variational-like inequality. By means of the Banach fixed-point theorem, we establish the existence and uniqueness of solution for the generalized nonlinear variational-like i...

In this paper, with the help of the duality operator and K. Fan’s lemma, we present existence results for strong vector equilibrium problems, under pseudomonotonicity assumptions and without any pseudomonotonicity assumptions, respectively. Then, as an application, the main results allow us to state existence theorems for strong vector variational inequality problems.

In this paper, we discuss two variants of the generalized nonlinear vector variational-like inequality problem. We provide their solutions by adopting topological approach. Topological properties such as compactness, closedness, and net theory are used in proof. The admissibility function space topology KKM-Theorem have played important role proving results.

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

In this study, generalized multivalued vector inverse quasi-variational inequality problems are developed, and error bounds obtained in terms of the residual gap function, regularized D-gap function. With help these constraints, one can effectively estimate distances between any feasible point solution set involving inequality.