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.
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. https://doi.org/10.3792/pjaa.76.153