Existence of solutions and convergence analysis for a system of quasivariational inclusions in Banach spaces

Abstract

In order to unify some variational inequality problems, in this paper, a new system of generalized quasivariational inclusion (for short, (SGQVI)) is introduced. By using Banach contraction principle, some existence and uniqueness theorems of solutions for (SGQVI) are obtained in real Banach spaces. Two new iterative algorithms to find the common element of the solutions set for (SGQVI) and the fixed points set for Lipschitz mappings are proposed. Convergence theorems of these iterative algorithms are established under suitable conditions. Further, convergence rates of the convergence sequences are also proved in real Banach spaces. The main results in this paper extend and improve the corresponding results in the current literature. 2000 MSC: 47H04; 49J40.

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

“…Since Giannessi, vector variational inequalities were investigated by many authors in abstract spaces and widely applied to transportation, finance, and economics, mathematical physics, engineering sciences and many others (see, for instance, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the reference therein).…”