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Hölder continuity of the unique solution to parametric vector quasiequilibrium problems via nonlinear scalarization

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Abstract

In this paper, by virtue of the nonlinear scalarization function commonly known as the Gerstewitz function in the theory of vector optimization, Hölder continuity of the unique solution to a parametric vector quasiequilibrium problem is studied based on nonlinear scalarization approach, under three different kinds of monotonicity hypotheses. The globally Lipschitz property of the nonlinear scalarization function is fully employed. Our approach is totally different from the ones used in the literature, and our results not only generalize but also improve the corresponding ones in some related works.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    C. R. Chen

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  1. C. R. Chen
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Correspondence to C. R. Chen.

Additional information

This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 11026144 and 11171362), a grant from the Ph.D. Programs Foundation of Ministry of Education of China (Grant number: 20100191120043) and the Fundamental Research Funds for the Central Universities (Grant number: CDJZR10 10 00 04).

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Chen, C.R. Hölder continuity of the unique solution to parametric vector quasiequilibrium problems via nonlinear scalarization. Positivity 17, 133–150 (2013). https://doi.org/10.1007/s11117-011-0153-5

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  • DOI: https://doi.org/10.1007/s11117-011-0153-5

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