Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities

Yang, Xiaoqi; Yao, Jen‐Chih

doi:10.1023/a:1020844423345

Cited by 80 publications

(41 citation statements)

References 8 publications

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“…Moreover, Corollary 2 generalizes Corollary 2.2 of [21] to the GVELPs. It also improves and extends Theorems 2.1, 2.2 and 3.1 of [19], Theorem 3.1 of [32] and Theorem 3.4 of [23] because the problems considered in our Corollary 2 are the more general problems, i.e., GVELPs.…”

Section: Definitionsupporting

confidence: 60%

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On generalized vector equilibrium-like problem in topological vector spaces

Ceng¹,

Liou²,

Pang³

et al. 2017

MMN

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Abstract. In this paper, some existence results for generalized vector equilibrium-like problems (for short, GVELPs) are established by virtue of a generalized KKM-Fan theorem in topological vector spaces. In addition, some applications to vector optimization problems are also given. The results presented in this paper are the extension and improvement of the corresponding results of other authors.

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Section: Definitionsupporting

confidence: 60%

“…As another consequence of Theorem 2, when˚is relaxed˛-f -pseudomonotone with respect to T and A, we also obtain a generalized version of Theorems 3.1-3.4 in [25] and hence Theorem 3.2 in [32]. Proof.…”

Section: Definitionmentioning

confidence: 58%

On generalized vector equilibrium-like problem in topological vector spaces

Ceng¹,

Liou²,

Pang³

et al. 2017

MMN

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show abstract

“…Later, many authors have investigated vector variational inequality problems in abstract spaces, see [1,13,19,20,24,26,27,29,30,31,35,36,38]. With the development of the theory about vector variational inequality problems, it has been seen that vector variational inequality problems have many important applications in vector optimization problems, see [25,37], vector equilibria problems, see [2,3,4,5,6,7,8,10,11,15,17,21,22,28,32,33,34,39], variational relation problems, see [17,18,23] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On the Lower Semicontinuity of the Solution Sets for Parametric Generalized Vector Mixed Quasivariational Inequality Problems

Hùng¹

2015

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we establish sufficient conditions for the solution set of parametric generalized vector mixed quasivariational inequality problem to have the semicontinuities such as the inner-openness, lower semicontinuity and Hausdorff lower semicontinuity. Moreover, a key assumption is introduced by virtue of a parametric gap function by using a nonlinear scalarization function. Then, by using the key assumption, we establish condition (H h (γ 0 , λ 0 , µ 0 )) is a sufficient and necessary condition for the Hausdorff lower semicontinuity, continuity and Hausdorff continuity of the solution set for this problem in Hausdorff topological vector spaces with the objective space being infinite dimensional. The results presented in this paper are different and extend from some main results in the literature.

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“…Many important results on existences and stabilities for various kinds of vector variational inequalities have been established, see e.g. [3,4,5,7,9,10,15,17] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A method of differential and sensitivity properties for weak vector variational inequalities

Guo¹,

Zeng²,

Sun³

et al. 2015

J. Nonlinear Sci. Appl.

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In this paper, by virtue of a contingent derivative and a Φ-contingent cone, we investigate differential properties of a class of set-valued maps in a more general setting utilizing Hadamard directional differentials. Then, by means of a gap function, sensitivity properties are discussed for a weak vector variational inequality. We also show that our results extend some existing results in the literature.

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Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities

Cited by 80 publications

References 8 publications

On generalized vector equilibrium-like problem in topological vector spaces

On generalized vector equilibrium-like problem in topological vector spaces

On the Lower Semicontinuity of the Solution Sets for Parametric Generalized Vector Mixed Quasivariational Inequality Problems

A method of differential and sensitivity properties for weak vector variational inequalities

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