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Fan’s inequalities for vector-valued multifunctions. (English) Zbl 0968.49014

Summary: 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.

MSC:

49J40 Variational inequalities
49J53 Set-valued and variational analysis
47H04 Set-valued operators
47H10 Fixed-point theorems
49J35 Existence of solutions for minimax problems
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