The proof of Kakutani's theorem is based on Brouwer's Fixed point theorem.Hence, we can consider kakutan's FPT as an application/a corollary/ of Brouwer's FPT. On the other hand, we can deduce Brouwer's Fixed point Theorem from kakutan's Fixed point theorem. Thus, they are equivalent. Every problem that can be solved using Kakutani's FPT can be solved by using Brouwer's FPT and vice versa. So, can we say kakutani's FPT is a real generalization of Brouwer's FPT?

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