Proceedings of the Japan Academy, Series A, Mathematical Sciences

Fan's inequalities for vector-valued multifunctions

Pando Grigorov Georgiev and Tamaki Tanaka

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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

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

First available in Project Euclid: 23 May 2006

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Zentralblatt MATH identifier

Primary: 49J53: Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]
Secondary: 49J35: Minimax problems 47H04: Set-valued operators [See also 28B20, 54C60, 58C06]

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


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.

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