On generalized vector mixed variational-like inequalities with complete semicontinuity

Lu Chuan Ceng; Qamrul Hasan Ansari; Jen Chih Yao

On generalized vector mixed variational-like inequalities with complete semicontinuity

Lu Chuan Ceng
, Qamrul Hasan Ansari
, Jen Chih Yao^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

Abstract

The purpose of this paper is to study the solvability for a class of generalized vector mixed variational-like inequalities (for short, GVMVLI) in Banach spaces. We first introduce the concepts of locally complete semicontinuity and globally complete semicontinuity for vector multifunctions. Utilizing Brouwer's fixed point theorem, we derive the solvability for this class of GVMVLIs with locally complete semicontinuity for vector multifunctions. On the other hand, by using Ky Fan's lemma we also prove the solvability for this class of GVMVLIs with globally complete semicontinuity for vector multifunctions. The results presented in this paper are the extension and improvement of some earlier and recent results in the literature.

Original language	English
Pages (from-to)	727-747
Number of pages	21
Journal	Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Volume	18
Issue number	6
State	Published - 2011

Keywords

Brouwer's fixed point theorem
Generalized vector mixed variational-like inequality
Globally complete semicontinuity
Ky Fan's lemma
Locally complete semicontinuity

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

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title = "On generalized vector mixed variational-like inequalities with complete semicontinuity",

abstract = "The purpose of this paper is to study the solvability for a class of generalized vector mixed variational-like inequalities (for short, GVMVLI) in Banach spaces. We first introduce the concepts of locally complete semicontinuity and globally complete semicontinuity for vector multifunctions. Utilizing Brouwer's fixed point theorem, we derive the solvability for this class of GVMVLIs with locally complete semicontinuity for vector multifunctions. On the other hand, by using Ky Fan's lemma we also prove the solvability for this class of GVMVLIs with globally complete semicontinuity for vector multifunctions. The results presented in this paper are the extension and improvement of some earlier and recent results in the literature.",

keywords = "Brouwer's fixed point theorem, Generalized vector mixed variational-like inequality, Globally complete semicontinuity, Ky Fan's lemma, Locally complete semicontinuity",

author = "Ceng, \{Lu Chuan\} and Ansari, \{Qamrul Hasan\} and Yao, \{Jen Chih\}",

year = "2011",

language = "English",

volume = "18",

pages = "727--747",

journal = "Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms",

issn = "1492-8760",

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number = "6",

}

TY - JOUR

T1 - On generalized vector mixed variational-like inequalities with complete semicontinuity

AU - Ceng, Lu Chuan

AU - Ansari, Qamrul Hasan

AU - Yao, Jen Chih

PY - 2011

Y1 - 2011

N2 - The purpose of this paper is to study the solvability for a class of generalized vector mixed variational-like inequalities (for short, GVMVLI) in Banach spaces. We first introduce the concepts of locally complete semicontinuity and globally complete semicontinuity for vector multifunctions. Utilizing Brouwer's fixed point theorem, we derive the solvability for this class of GVMVLIs with locally complete semicontinuity for vector multifunctions. On the other hand, by using Ky Fan's lemma we also prove the solvability for this class of GVMVLIs with globally complete semicontinuity for vector multifunctions. The results presented in this paper are the extension and improvement of some earlier and recent results in the literature.

AB - The purpose of this paper is to study the solvability for a class of generalized vector mixed variational-like inequalities (for short, GVMVLI) in Banach spaces. We first introduce the concepts of locally complete semicontinuity and globally complete semicontinuity for vector multifunctions. Utilizing Brouwer's fixed point theorem, we derive the solvability for this class of GVMVLIs with locally complete semicontinuity for vector multifunctions. On the other hand, by using Ky Fan's lemma we also prove the solvability for this class of GVMVLIs with globally complete semicontinuity for vector multifunctions. The results presented in this paper are the extension and improvement of some earlier and recent results in the literature.

KW - Brouwer's fixed point theorem

KW - Generalized vector mixed variational-like inequality

KW - Globally complete semicontinuity

KW - Ky Fan's lemma

KW - Locally complete semicontinuity

UR - https://www.scopus.com/pages/publications/84855383989

M3 - Article

AN - SCOPUS:84855383989

SN - 1492-8760

VL - 18

SP - 727

EP - 747

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

IS - 6

ER -

On generalized vector mixed variational-like inequalities with complete semicontinuity

Abstract

Keywords

ASJC Scopus subject areas

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