Nonlinear scalarization with applications to Hölder continuity of approximate solutions

Lili Li; Chunrong Chen

doi:10.3934/naco.2014.4.295

Article Contents

2014, Volume 4, Issue 4: 295-307. Doi: 10.3934/naco.2014.4.295

This issue Previous Article Strong convergence of an implicit iteration process for a finite family of Lipschitz $\phi -$uniformly pseudocontractive mappings in Banach spaces Next Article Topological properties of Henig globally efficient solutions of set-valued problems

Nonlinear scalarization with applications to Hölder continuity of approximate solutions

Lili Li^1, and
Chunrong Chen^2,

1.
College of Mathematics and Statistics, Chongqing University, Chongqing 401331
2.
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331

Received: May 2014

Revised: September 2014

Published: December 2014

Abstract / Introduction Related Papers Cited by

Abstract

In this article, firstly, some useful properties of the Gerstewitz scalarizing function are discussed, such as its globally Lipschitz property, concavity and monotonicity. Secondly, as an application of these properties, verifiable sufficient conditions for Hölder continuity of approximate solutions to parametric generalized vector equilibrium problems are established via Gerstewitz scalarizations. Moreover, some examples are provided to illustrate our main conclusions in the vector settings.

Keywords:

Nonlinear scalarization,
Hölder continuity,
parametric generalized vector equilibrium problems,
approximate solutions,
globally Lipschitz property.

Mathematics Subject Classification: Primary: 49K40; Secondary: 90C31.

Citation:

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