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

Hölder continuity of the unique solution to parametric vector quasiequilibrium problems via... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

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

Positivity , Volume 17 (1) – Jan 11, 2012
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Publisher
SP Birkhäuser Verlag Basel
Copyright
Copyright © 2011 by Springer Basel AG
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-011-0153-5
Publisher site
See Article on Publisher Site

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.

Journal

PositivitySpringer Journals

Published: Jan 11, 2012

References

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