Eysteinn Óláfsson

http://fmg.ac/Projects/MedLands/IRELAND.htm#_Toc389126206

m [firstly] ---. The name of Olaf´s [first] wife is not known.

Olaf & his [first] wife had two children:

1. CARLUS (-killed in battle 866). The Annals of the Four Masters record in 866 “Carlus son of Amhlaeibh” among those killed in a battle fought between "Flann son of Conaing lord of all Breagh…the men of Breagh and Leinster and the foreigners" and Aedh King of Ireland at "Cill Ua nDaighre"[1159].
2. EYSTEIN [Oistin] (-killed 875). [The Fragmentary Annals of Ireland record in [871/72] that "Imar son of Gothfraid son of Ragnall son of Gothfraid Conung son of Gofraid" and "the son of the man who left Ireland" [Olaf/Amlaib] "plundered from west to east and from south to north"[1160]. It is possible that this passage refers to Eystein or another son.] The Annals of Ulster record in 875 that "Oistin son of Amlaib, king of the Norsemen, was deceitfully killed by Albann"[1161].

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https://en.wikipedia.org/wiki/Oistin_mac_Amla%C3%ADb

Oistin mac Amlaíb (Old Norse: Eysteinn Óláfsson) was a ninth-century Norse or Norse-Gael leader who is sometimes identified as a King of Dublin. He was a son of Amlaíb Conung and nephew of Ímar, founder of the Uí Ímair dynasty. He is sometimes identified with Thorstein the Red, a figure who features in the Norse sagas.

Family

Amlaíb Conung is identified as Oistin's father by the Annals of Ulster.[19] A brother, Carlus, is mentioned by the Annals of the Four Masters.[20]

A number of other familial connections are known if the identification of Oistin with Thorstein the red is correct. According to the sagas, Aud the Deep-Minded, daughter of Ketil Flatnose, the King of Isles, was the mother of Thorstein.[21] Thorstein's wife is given as Thurid (Þuríður in Old Norse), the daughter of a Geatish man named Eyvind the Easterner. Their children include at least six daughters, Osk, Vigdis, Olof, Thorhild and Thorgerd, and at least one son, Olaf Feilan.[22]