Dear All,
Why most mathematicians choose kkm-mapping to solve the problems in variational inequality ? while the problems can been solve by another methods such as fixed point theorem, critical point theorems and so on.
best regards
How are you sure that all VI problems are solved by KKM? have you read the book by Facchinei and pang? i have seen several usages of fixed point theorem to the existance and uniqueness of the solutions.
Dear Prof B. Mahboobi, i dont say all problem can be solved by KKM, but i say most mathematicians choose kkm-mapping to solve the problems in variational inequality, but i have answer from prof Costea (It is proved by Tarafdar that Fan's version of the KKM Theorem is equivalent with a Fixed Point Theorem for multifunctions, so it is a matter of choice).
best regards
yes ! that is right too! I forget the fan's theorem.
http://www.sciencedirect.com/science/article/pii/0022247X87901983
are you interested in fixed point theorem on functional spaces ? and also on probability spaces ?
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