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Semicontinuity of solution mappings of parametric generalized strong vector equilibrium problems. (English) Zbl 1158.49017
Summary: We study the $\varepsilon$-Generalized Strong Vector Equilibrium Problem ($\varepsilon$-GSVEP) and $\varepsilon$-Extended Vector Equilibrium Problem ($\varepsilon$-ESVEP) which can be regarded as approximate problems to the generalized strong vector equilibrium problems (GSVEP). Existence results for $\varepsilon$-GSVEP and $\varepsilon$-ESVEP are established. We also investigate various continuities of the solution mappings of $\varepsilon$-GSVEP and $\varepsilon$-ESVEP, respectively.

MSC:
49J45Optimal control problems involving semicontinuity and convergence; relaxation
49K40Sensitivity, stability, well-posedness of optimal solutions
90C31Sensitivity, stability, parametric optimization
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