Solution continuity of parametric generalized vector equilibrium problems with strictly pseudomonotone mappings

Xin Zuo; Chun-Rong Chen; Hong-Zhi Wei

doi:10.3934/jimo.2016027

Article Contents

2017, Volume 13, Issue 1: 477-488. Doi: 10.3934/jimo.2016027

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Solution continuity of parametric generalized vector equilibrium problems with strictly pseudomonotone mappings

College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

* Corresponding author: Chun-Rong Chen
* Corresponding author: Chun-Rong Chen

Received: January 2015

Published: August 2017

This research was supported by the National Natural Science Foundation of China (Grant numbers: 11301567 and 11026144) and the Fundamental Research Funds for the Central Universities (Grant number: 106112015CDJXY100002).

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Abstract

In this paper, new continuity (both lower and upper semicontinuities) results of solution mappings to parametric generalized (strong) vector equilibrium problems are established by scalarization approaches, under $f$-strict pseudomonotonicity assumptions. Especially, based on this new kind of monotonicity, the compactness of the mapping $F$ is not required, which is different from the related literature. Some examples are also provided to illustrate main conclusions.

Keywords:

Semicontinuity,
parametric generalized (strong) vector equilibrium problems,
scalarization,
strict pseudomonotonicity.

Mathematics Subject Classification: Primary: 49K40, 90C31; Secondary: 47J20.

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