Taiwanese Journal of Mathematics


Jia-wei Chen and Yeong-Cheng Liou

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In this article, we investigate the existence of solutions and Levitin-Polyak well-posedness for a class of system of parametric strong quasi-equilibrium problems (SPSQEP) involving set-valued mappings in Hausdorff topological vector spaces. The existence of solutions to the problem (SPSQEP) are presented, and then the notions of Levitin-Polyak well-posedness and generalized Levitin-Polyak well-posedness for (SPSQEP) are introduced. Moreover, some metric characterizations of these well-posedness are derived under quite mild conditions. The relationships between these well-posedness of (SPSQEP) and the existence and uniqueness of its solutions are established. Finally, some examples are given to illustrate the presented results.

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Taiwanese J. Math., Volume 18, Number 2 (2014), 337-355.

First available in Project Euclid: 10 July 2017

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Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 49K40: Sensitivity, stability, well-posedness [See also 90C31] 90C33: Complementarity and equilibrium problems and variational inequalities (finite dimensions)

system of parametric strong set-valued quasi-equilibrium problem Levitin-Polyak well-posedness generalized Levitin-Polyak well-posedness Hausdorff metric Kuratowski measure of noncompactness


Chen, Jia-wei; Liou, Yeong-Cheng. SYSTEMS OF PARAMETRIC STRONG QUASI-EQUILIBRIUM PROBLEMS: EXISTENCE AND WELL-POSEDNESS ASPECTS. Taiwanese J. Math. 18 (2014), no. 2, 337--355. doi:10.11650/tjm.18.2014.3495. https://projecteuclid.org/euclid.twjm/1499706390

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