Strong vector equilibrium problems with LSC approximate solution mappings

Nguyen Ba Minh; Pham Huu Sach

doi:10.3934/jimo.2018165

Article Contents

2020, Volume 16, Issue 2: 511-529. Doi: 10.3934/jimo.2018165

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Strong vector equilibrium problems with LSC approximate solution mappings

Nguyen Ba Minh^1, and
Pham Huu Sach^2, ,

1.
Thuongmai University, Hanoi, Vietnam
2.
Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, 10307 Hanoi, Vietnam

* Corresponding author: Pham Huu Sach
* Corresponding author: Pham Huu Sach

Received: December 2017

Revised: June 2018

Early access: October 2018

Published: February 2020

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2016.11.

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Abstract

This paper introduces two classes of parametric strong vector equilibrium problems whose approximate solution mappings are lower semicontinuous. In the first class, the objective set-valued maps satisfy some cone-convexity/cone-concavity assumptions, and in the second one, they satisfy some strongly proper cone-quasiconvexconcavity assumptions. All these mentioned concepts of generalized cone-convexity/cone-concavity/ strongly proper cone-quasiconvexconcavity are new and different from the traditional ones. Some upper semicontinuity/continuity results are also obtained. Applications to parametric weak u-set and l-set optimization problems and weak vector multivalued equilibrium problems are given.

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Mathematics Subject Classification: Primary: 49K40, 90C29, 90C31.

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