On the Hölder continuity of solution maps to parametric generalized vector quasi-equilibrium problems via nonlinear scalarization

Rabian Wangkeeree,Pakkapon Preechasilp

doi:10.1186/1029-242x-2014-425

Rabian Wangkeeree, Pakkapon Preechasilp

Open Access

https://doi.org/10.1186/1029-242x-2014-425

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Abstract

In this paper, by using a nonlinear scalarization technique, we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric generalized vector quasi-equilibrium problem with set-valued mappings. The results are different from the recent ones in the literature.

Highlights

1 Introduction The generalized vector quasi-equilibrium problem is a unified model of several problems, namely generalized vector quasi-variational inequalities, vector quasi-optimization problems, traffic network problems, fixed point and coincidence point problems, etc
It is well known that the stability analysis of a solution mapping for equilibrium problems is an important topic in optimization theory and applications
There have been many papers to discuss the stability of solution mapping for equilibrium problems when they are perturbed by parameters ( known the parametric equilibrium problems)

Summary

Introduction

The generalized vector quasi-equilibrium problem is a unified model of several problems, namely generalized vector quasi-variational inequalities, vector quasi-optimization problems, traffic network problems, fixed point and coincidence point problems, etc. (see, for example, [ , ] and the references therein). Question Can one establish the Hölder continuity of a solution mapping to the parametric generalized vector quasi-equilibrium problem with set-valued mappings by using a nonlinear scalarization method?

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Results

Conclusion