## Taiwanese Journal of Mathematics

### THE $(S)_+$-CONDITION FOR VECTOR EQUILIBRIUM PROBLEMS

Y. Chiang

#### Abstract

In this paper, we generalize the $(S)_+$-condition to bifunctions with values in an oredered Hausdorff topological vector space $\mathcal{Z}$, and define a weak $(S)_+$-condition for the bifunctions. These conditions extend naturally to operators from nonempty subsets of a topological vector space $X$ into the set $\mathcal{L}(X,\mathcal{Z})$ of all continuous linear mappings from $X$ into $\mathcal{Z}$. Then we derive some existence results for vector equilibrium problems and vector variational inequalities associated with bifunctions or operators satisfying the weak $(S)_+$-condition.

#### Article information

Source
Taiwanese J. Math., Volume 10, Number 1 (2006), 31-43.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500403797

Digital Object Identifier
doi:10.11650/twjm/1500403797

Mathematical Reviews number (MathSciNet)
MR2186160

Zentralblatt MATH identifier
1117.49020

#### Citation

Chiang, Y. THE $(S)_+$-CONDITION FOR VECTOR EQUILIBRIUM PROBLEMS. Taiwanese J. Math. 10 (2006), no. 1, 31--43. doi:10.11650/twjm/1500403797. https://projecteuclid.org/euclid.twjm/1500403797