Levitin-Polyak well-posedness for lexicographic vector equilibrium problems

Volume 10, Issue 2, pp 354--367 http://dx.doi.org/10.22436/jnsa.010.02.02

Publication Date: February 20, 2017 Submission Date: August 13, 2016

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Authors

Rabian Wangkeeree - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand. - Research Center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok 65000, Thailand. Thanatporn Bantaojai - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.

Abstract

We introduce the notions of Levitin-Poljak (LP) well-posedness and LP well-posedness in the generalized sense for the lexicographic vector equilibrium problems. Then, we establish some sufficient conditions for lexicographic vector equilibrium problems to be LP well-posedness at the reference point. Numerous examples are provided to explain that all the assumptions we impose are very relaxed and cannot be dropped. The results in this paper unify, generalize and extend some known results in the literature.

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Keywords

• Levitin-polyak well-posedness
• lexicographic vector equilibrium problems
• metric spaces.

MSC

•  90C33
•  49K40

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