Questions & Answers about Kütüphaneye gelmişken bu kitabı da geri vereyim.
Because gelmek normally takes the dative case when it means to come to a place.
- kütüphane = library
- kütüphaneye = to the library
So:
- Kütüphaneye gelmek = to come to the library
The ending is -(y)e / -(y)a, the Turkish dative suffix. The extra y appears because the noun ends in a vowel.
Gelmişken means something like:
- since I’ve come
- now that I’m here
- while I’m at it, since I came
It often gives an opportunity or might as well feeling. The speaker is saying that coming to the library creates a good chance to do one more thing.
So the idea is not just I came, but more like:
- Since I’m already here, I may as well return this book too.