I think the question is a bit badly defined, but I will give you the answer for which island country lies in the eastern part of the Mediterranean and which island country lies in the Persian Gulf.
1. The island country that lies in the eastern part of the Mediterranean is the country of Cyprus.
Cyprus is a small island country in the eastern part of the Mediterranean, and it geographically falls under Asia, while politically and culturally is a European country. The country mainly functions around the tourism.
2. The island country that lies in the Persian Gulf is the country of Bahrain.
Bahrain is a small island country in the Persian Gulf, and it falls into Asian territory, both geographically, and politically and culturally. It is a country that is mainly based around the oil and gas industry.
