-men, in some accents, is short form of -meyin.

gitmen (gitmeyin), kalman (kalmayın)

değmen benim ... - don´t touch my ...

But if you place possessive adjective before the word, the meaning changes:

senin değmen - your touch

değ(mek) => touch (verb)

değ-me => touch(ing) (noun)

benim değmem

senin değmen

onun değmesi

bizim değmemiz

sizin değmeniz

onların değmesi/değmeleri

Vallah the last thing is what I was thinking about.

But later on I thought, people use it like benim değmem senin değmen but it actually has to be benim değmenim senin değmenin etc...

So anyway it wouldnt be correct..

I just checked with my husband and he explained me there isnt anything like değmenim değmenim because of not being a property. So I am all wrong here.

Anyway sorry I didnt want to confuse you all 

Don´t worry, Melike, we are all learning here. Thank you all for your comments, it is interesting that "colloquial" "değmen" can in fact mean "değmeyin" (I wonder if I could ever read about it in some grammar book...)