## Abstract and Applied Analysis

### Existence Solutions of Vector Equilibrium Problems and Fixed Point of Multivalued Mappings

#### Abstract

Let $K$ be a nonempty compact convex subset of a topological vector space. In this paper-sufficient conditions are given for the existence of $x\in K$ such that $F(T)\cap \text{V}\text{E}\text{P}(F)\ne \varnothing$, where $F(T)$ is the set of all fixed points of the multivalued mapping $T$ and $\text{VEP}(F)$ is the set of all solutions for vector equilibrium problem of the vector-valued mapping $F$. This leads us to generalize and improve some existence results in the recent references.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 952021, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393442755

Digital Object Identifier
doi:10.1155/2013/952021

Mathematical Reviews number (MathSciNet)
MR3034898

Zentralblatt MATH identifier
1262.47080

#### Citation

Sitthithakerngkiet, Kanokwan; Plubtieng, Somyot. Existence Solutions of Vector Equilibrium Problems and Fixed Point of Multivalued Mappings. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 952021, 6 pages. doi:10.1155/2013/952021. https://projecteuclid.org/euclid.aaa/1393442755

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