Stability of solution mapping for parametric symmetric vector equilibrium problems

Xiao-Bing Li; Xian-Jun Long; Zhi Lin

doi:10.3934/jimo.2015.11.661

Article Contents

2015, Volume 11, Issue 2: 661-671. Doi: 10.3934/jimo.2015.11.661

This issue Previous Article Neural network smoothing approximation method for stochastic variational inequality problems Next Article Scalarizations and Lagrange multipliers for approximate solutions in the vector optimization problems with set-valued maps

Stability of solution mapping for parametric symmetric vector equilibrium problems

1.
College of Sciences, Chongqing Jiaotong University, Chongqing, 400074
2.
College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067

Received: September 30, 2013

Revised: April 30, 2014

Published: March 2015

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Abstract

This paper is concerned with the stability for a parametric symmetric vector equilibrium problem. A parametric gap function for the parametric symmetric vector equilibrium problem is introduced and investigated. By virtue of this function, we establish the sufficient and necessary conditions for the Hausdorff lower semicontinuity of solution mapping to a parametric symmetric vector equilibrium problem. The results presented in this paper generalize and improve the corresponding results in the recent literature.

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Mathematics Subject Classification: 34D10, 46N10, 49K40, 91B50.

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