Stability analysis for parametric generalized vector quasi-variational-like inequality problems

Abstract

In this article, we consider a class of parametric generalized vector quasi-variationallike inequality problem (for short, (PGVQVLIP)) in Hausdorff topological vector spaces, where the constraint set K and a set-valued mapping T are perturbed by different parameters, and establish the nonemptiness and upper semicontinuity of the solution mapping S for (PGVQVLIP) under some suitable conditions. By virtue of the gap function, sufficient conditions for the H-continuity and B-continuity of the solution mapping S of (PGVQVLIP) are also derived. Moreover, examples are provided for illustrating the presented results. 2000 Mathematics Subject Classification: 49J40; 90C33.

Strong convergence theorems for equilibrium problems and weak Bregman relatively nonexpansive mappings in Banach spaces

“…1 Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA. 2 Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah, 21589, Saudi Arabia. 3 College of Sciences, Northwest A&F University, Yangling, Xianyang, Shaanxi 712100, China.…”

Vector variational inequalities and related topics: A survey of theory and applications

“…Within the last years, several authors have investigated the stability analysis of problem (2.2), that is, the qualitative analysis of several properties of the solution mapping Sol : U × V ⇒ R l . These include, for example, the upper semicontinuity, the lower semicontinuity, the (lipschitz) continuity and the Robinson's metric regularity property of Sol; see [1,49,52,58,86,89,124]. In this research area, scalarization techniques [52,85,141] and gap functions [47] have proven to be powerful tools.…”

Vector parametric quasi-equilibrium problems for the sum of two set-valued mappings

“…then we obtain parametric generalized vector quasi-variational-like inequality problem in [21]; (iv) if for each x, y ∈ A and p ∈ P, we define G(x, y, p) = 0, then (a) Problem (P β (p)) reduces to vector parametric equilibrium problems, which has been considered in, e.g., [9,10,11,12,13,17,22]; (b) if F(x, y, p) = H(y, p) − H(x, p), that H : A × P −→ 2 Z then, we have vector parametric optimization problem (see [16,18,23]); (c) if F(x, y, p) =< w, y − x >, such that T : A × P −→ 2 L(X,Z) and w ∈ T (x, p) then we obtain vector parametric variational inequality (see [23,24]).…”