(is this sentence grammatically and logically correct or not?)
no one cannot admit that i am the best artist he has ever seen.
i am confused because of the double negative.

No one cannot admit that I am the best artist he has ever seen.

Grammatically and logically, this is fine, but it does not scan well at all, and it might not be want you want to say. Don't forget double negatives are not always wrong. For example: She is not unattractive.

I suspect you mean:

No one can admit that I am the best artist he has ever seen.

The other issue is using no one being the antecedent of he. This is also acceptable. The alternatives are to use they, but that is grammatically flawed or he/she, but that is clumsy.

Everyone will concede I am the best artist he has ever seen.

I think this is clearer. When formal or technical writing, it is preferable to use plain, simple English. When creative writing, some may find mind boggling double negatives interesting.