This is the 1310th most frequent Russian word.
собственной
"Own" or "personal."
Here, 'собственной' is used as an adjective to emphasize ownership and personal possession, modifying the noun 'библиотеки' (library).
Я купила книгу для своей собственной библиотеки.
I bought a book for my own library.
'Собственной' here functions to stress the personal initiative, enhancing the possessive sense of 'инициативе' (initiative).
Это сделано по моей собственной инициативе.
This was done on my own initiative.
In this sentence, 'собственной' modifies 'идеи' (idea) to specify that it uniquely belongs to the subject, reinforcing ownership and origination.