Open Access
Nov. 2000 Fan's inequalities for vector-valued multifunctions
Pando Grigorov Georgiev, Tamaki Tanaka
Proc. Japan Acad. Ser. A Math. Sci. 76(9): 153-157 (Nov. 2000). DOI: 10.3792/pjaa.76.153


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.


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Pando Grigorov Georgiev. Tamaki Tanaka. "Fan's inequalities for vector-valued multifunctions." Proc. Japan Acad. Ser. A Math. Sci. 76 (9) 153 - 157, Nov. 2000.


Published: Nov. 2000
First available in Project Euclid: 23 May 2006

zbMATH: 0968.49014
MathSciNet: MR1801678
Digital Object Identifier: 10.3792/pjaa.76.153

Primary: 49J53
Secondary: 47H04 , 49J35

Keywords: Fan's inequality , quasiconvex functions , semicontinuous mappings , vector-valued multifunctions

Rights: Copyright © 2000 The Japan Academy

Vol.76 • No. 9 • Nov. 2000
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