I have yet to meet 'anyone' ...

[nyota]

I have yet to meet anyone who can run as fast as him.

Could I say, I have yet to meet someone who ... ?

[Khosro]

I have yet to meet anyone who can run as fast as him.

Could I say, I have yet to meet someone who ... ?

What's the difference in your opinion?

I think in the first sentence you just want to show your admire for him.
In the second sentence you are perhaps a running coach and have recently lost your best runner and looking for a suitable substitute.

[susiedqq]

Either could be used, however in this context:

anyone = out of every person you can even think of

someone = more specifically an unknwon person

[nyota]

What's the difference in your opinion?

Khosro, I wasn't reallly thinking of any differences. I wasn't even sure if 'someone' was possible. ;)

someone = more specifically an unknwon person

I don't quite get this one?

[5jj]

1. I have yet to meet anyone who can run as fast as him.
2. I have yet to meet someone who ... ?

In #1, 'anyone' is unrestricted - we may infer that the speaker is suggesting that s/he has tried all the possibilties.

In#2, 'someone' is more restricted; we may infer that the speaker is suggesting that s/he has not (yet) tried all the possibilities.

Michael Lewis [The English Verb, (1986), Hove: LTP] wrote:

“Both some and any are used with indefinite reference.
Some is used if the idea is restricted or limited in some way.
Any is used if the idea is unrestricted or unlimited.
Any applies to all or none; some applies to part.

The restriction may be a real one – There’s some cheese in the fridge – or a psychological one, existing only in the mind of the speaker – Would you like something to eat?

The real semantic distinction is as simple as that, and applies to all uses of some and any.”

Lewis could have added, "and to all words begining with some or any - ~one, ~body, ~thing, ..."