Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures

Jing-Nan Li, San-Hua Wang and Yu-Ping Xu
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Jing-Nan Li: Department of Mathematics, Nanchang University, Nanchang 330031, China
San-Hua Wang: Department of Mathematics, Nanchang University, Nanchang 330031, China
Yu-Ping Xu: Department of Mathematics, Nanchang University, Nanchang 330031, China

Mathematics, 2020, vol. 8, issue 9, 1-17

Abstract: In this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed. By using the concept of cosmically upper continuity rather than the one of upper semicontinuity for cone-valued mapping, some existence theorems of solutions are established under suitable assumptions of cone-continuity and cone-convexity for the equilibrium mappings. Moreover, the results of compactness for solution sets are proven. As applications, some existence results of strong saddle points are obtained. The main results obtained in this paper unify and improve some recent works in the literature.

Keywords: symmetric generalized strong vector quasi-equilibrium problems; variable ordering structures; existence of solutions; cosmically upper continuity; fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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