This is the 9923rd most frequent Turkish word.
açtıkları
"Their opened" or "what they opened."
In this sentence, 'açtıkları' pertains to the book that was opened by them, referencing their action and describing the book.
Kardeşlerim açtıkları kitabı dikkatle inceliyordu.
My siblings were carefully examining the book they opened.
Here, 'açtıkları' refers to the flowers they have grown, and metaphorically 'opened' signifies the blooming aspect.
Bahçede açtıkları çiçekler baharı müjdeliyordu.
The flowers they cultivated in the garden heralded the spring.
In this usage, 'açtıkları' relates to the act of opening a store, indicating the store established by them.