Iterative Algorithm for Finding Approximate Solutions of a Class of Mixed Variational-like Inequalities

Abstract

The purpose of this paper is to investigate the iterative algorithm for finding approximate solutions of a class of mixed variational-like inequalities in a real Hilbert space, where the iterative algorithm is presented by virtue of the auxiliary principle technique. On one hand, the existence of approximate solutions of this class of mixed variational-like inequalities is proven. On the other hand, it is shown that the approximate solutions converge strongly to the exact solution of this class of mixed variational-like inequalities.

Iterative algorithm for finding approximate solutions of mixed quasi-variational-like inclusions

“…Problem (1.2) and its special cases have been introduced and studied by Ding [5][6][7] and Fang and Huang [8] in Banach spaces, and by Lee, Ansari and Yao [9], Ansari and Yao [10], Zeng [11] and Schaible, Yao and Zeng [12] in Hilbert spaces. Moreover, if N (T u, Au) = T u − Au for all u, v ∈ D, then the MQVLIP (1.1) is equivalent to finding u ∈ D, such that…”

A generalization of Minty's lemma and its applications to generalized mixed vector equilibrium problems

“…In recent years, variational inequalities have been generalized and extended in various different directions, see [1][2][3][4][5][6][7]. Moreover, many authors [4,[8][9][10][11][12][13] have investigated vector variational inequalities in abstract spaces.…”

Iterative algorithm for solving mixed quasi-variational-like inequalities with skew-symmetric terms in Banach spaces

“…The method based on auxiliary principle technique was first suggested by Glowinski et al [6] for solving variational inequalities in 1981. Subsequently, it has been used to solve a number of generalizations 2 Iterative algorithm for solving MQVLIP of classical variational inequalities; see, for example, [1,4,8,[14][15][16] and the references therein.…”