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Tykhonov Well-Posedness for Quasi-Equilibrium Problems

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Abstract

We consider an extension of the notion of Tykhonov well-posedness for perturbed vector quasi-equilibrium problems. We establish some necessary and sufficient conditions for verifying these well-posedness properties. As for applications of our results, the Tykhonov well-posedness of vector variational-like inequalities and vector optimization problems is established.

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Acknowledgments

The authors are grateful to Chief Editor and the reviewers for valuable comments and remarks. The second author was partially supported by the Center of Excellence for Mathematics, University of Isfahan, Iran.

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Authors and Affiliations

  1. Department of Mathematics, University of Isfahan, 81745-163, Isfahan, Iran

    M. Darabi

  2. Department of Mathematics, Sheikhbahaee University and University of Isfahan, Isfahan, Iran

    J. Zafarani

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  1. M. Darabi
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  2. J. Zafarani
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Correspondence to J. Zafarani.

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Communicated by Qamrul Hasan Ansari.

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Darabi, M., Zafarani, J. Tykhonov Well-Posedness for Quasi-Equilibrium Problems. J Optim Theory Appl 165, 458–479 (2015). https://doi.org/10.1007/s10957-014-0630-7

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