Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S705 - S718|
|Published online||02 March 2021|
On the existence and stability of solutions to stochastic equilibrium problems
Department of Mathematics, Teacher College, Can Tho University, Can Tho, Vietnam
2 Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology of Vietnam, Ho Chi Minh City, Vietnam
3 Department of Mathematics, Cantho College, Can Tho, Vietnam
* Corresponding author: email@example.com
Accepted: 22 December 2019
In this paper we consider stochastic equilibrium problems involving parameter of probability measures. Employing the fixed point theorem of Knaster, Kuratowski, Mazurkiewicz, and Fan (KKM-Fan), conditions for the existence of solutions to such problems are established. We then propose new metric concepts on the underlying stochastic spaces and study some properties corresponding to these metrics. Afterwards, we study sufficient conditions for the solution mappings of such problems, that are closed, upper (lower) semicontinuous and continuous with respect to the mentioned metrics. Finally, the special cases of stochastic optimization problems are taken into account as the applications.
Mathematics Subject Classification: 49K40 / 49K45 / 90C15 / 90C31
Key words: Stochastic equilibrium problems / stochastic optimization / probabilistic metric spaces / existence and stability conditions / closedness and upper (lower) semicontinuity/continuity
© EDP Sciences, ROADEF, SMAI 2021
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