## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Fan's inequalities for vector-valued multifunctions

#### Abstract

We present four variants of Fan's type inequality for vector-valued multifunctions in topological vector spaces with respect to a cone preorder in the target space, when the functions and the cone possess various kinds of semicontinuity and convexity properties. Using the classical scalar Fan inequality, we prove directly a two-function result of Simons, which is used to establish our main tool for proving the presented results.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 9 (2000), 153-157.

Dates
First available in Project Euclid: 23 May 2006

https://projecteuclid.org/euclid.pja/1148393432

Digital Object Identifier
doi:10.3792/pjaa.76.153

Mathematical Reviews number (MathSciNet)
MR1801678

Zentralblatt MATH identifier
0968.49014

#### Citation

Georgiev, Pando Grigorov; Tanaka, Tamaki. Fan's inequalities for vector-valued multifunctions. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 9, 153--157. doi:10.3792/pjaa.76.153. https://projecteuclid.org/euclid.pja/1148393432

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