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Most of them have concentrated on the authenticated key establishment problems for setting up a secure channel between IMD and programmer.
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See Paseau (2008) for discussion of this and other problems for set-theoretic reductionism.
To the best of authors' knowledge, there are few articles to investigate minimax problems for set-valued mappings.
Zhang et al. [20] investigated some minimax problems for set-valued mappings by applying the Fan-Browder Fixed Point Theorem.
On the other hand, various kinds of differentiable type dual problems for set-valued optimization problems, such as Mond-Weir type and Wolfe type dual problems, have been investigated.
Since Kuroiwa [11] investigated minimax problems of set-valued mappings in 1996, many authors have devoted their efforts to the study of the minimax problems for set-valued mappings.
We discuss the minimax problems for set-valued mappings with several hierarchical structures, and scalar hierarchical minimax theorems, hierarchical minimax theorems, hierarchical minimax inequalities for set-valued mappings, and the existence of cone-saddle points.
This leaves unresolved the problem of setting independent values for the two parameters.
Then we consider the best approximation problem and the best proximity problem for set-valued mappings that are condensing.
An important problem for set-valued monotone mappings is to find (bar{x}in H) such that (0in Bbar{x}).
An important problem for set-valued monotone mappings is to find x ¯ ∈ H such that 0 ∈ B x ¯.
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