Gap functions for a system of generalized vector quasi-equilibrium problems with set-valued mappings |
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| Authors: | Nan-jing Huang Jun Li Soon-yi Wu |
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| Affiliation: | (1) Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, P.R. China;(2) School of Mathematics and Information, China West Normal University, Nanchong, Sichuan, 637002, P.R. China;(3) Institute of Applied Mathematics, National Cheng-Kung University, Tainan, 700, Taiwan;(4) National Center for Theoretical Sciences, Tainan, Taiwan |
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| Abstract: | In this paper, some gap functions for three classes of a system of generalized vector quasi-equilibrium problems with set-valued mappings (for short, SGVQEP) are investigated by virtue of the nonlinear scalarization function of Chen, Yang and Yu. Three examples are then provided to demonstrate these gap functions. Also, some gap functions for three classes of generalized finite dimensional vector equilibrium problems (GFVEP) are derived without using the nonlinear scalarization function method. Furthermore, a set-valued function is obtained as a gap function for one of (GFVEP) under certain assumptions. |
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| Keywords: | System of generalized vector quasi-equilibrium problems Gap function Nonlinear scalarization function Set-valued mapping |
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