This is the 250th most frequent Turkish word.
olmayan
"Nonexistent" or "not present."
Here, 'olmayan' is used as a descriptive adjective meaning 'that doesn't exist' to modify 'durum' (situation).
Olmayan bir durum için endişelenme.
Don't worry about a situation that doesn't exist.
In this sentence, 'olmayan' describes 'kitapları' (books) and means 'not in' or 'not present in' the bookshelf.
Kitaplıkta olmayan kitapları sorabilir miyim?
Can I ask about the books that are not in the bookshelf?
Here, 'olmayan' refers to things 'not being in possession' and modifies 'şeyler' (things).