Is it correct?

[Raksmey]

Hi all of you out there!! I have been away from this site for quite a while. And now i am back. OK, let's go the point. I have something to ask all of you. Everytime i watch English-speaking movies, i see the people use the sentence:

"Don't you worry about this..." This is not a question actually.

And i think it carries the same meaning as

"Don't worry about this..."

My question is whether it is correct to say so?
And is it correct to use it writing.
And what is the sentence like this called? Inversion?
OK, i might be asking too many questions, but those are what i don't understand
Hope all of you guys will share some ideas about it.

[Tdol]

It is correct and it isn't inversion.  Normally, we don't include a subject pronoun when we use the imperative (http://www.usingenglish.com/glossary/imperative.html) as the subject is understood.  When we include it, it can have a slightly different meaning:
Don't worry about this.  (=you shouldn't worry about this)
Don't you worry about this. (=it's my responsibility and I will take care of it.)
 

[Raksmey]

Thank you Tdol. Anyway, you have just touched on one point. Another point is whether we can use such sentence in writing.

Hope to hear your addition response soon

[Tdol]

There's no reason why not, but it would have to be a piece of writing where we are talking that directly to the  reader.