Jocelyn, welcome to Istanbul.
The most cost efficient transfer is by public transport. First get an Istanbulkart at the metro station at the airport, load it with fares, and get on the metro and get off at Zeytinburnu. There take the Kabatas tram (T1) and get off at Gulhane stop. Yasmak Sultan Hotel is 3 minutes walk from the Gulhane tram stop. Total cost with Istanbulkart is 3.20 TL (1.8 USD).
Thankyou so much.
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