Snorre names "Eirik the Victorious and Olaf, the father of Styrbjorn" as the sons of Bjorn Eriksson.
According to Saxo Grammaticus, Erik was the son of Olof and deposed his cousin Styrbjörn in [984/85], succeeding as ERIK "Segersäll/the Victorious" King of Sweden. Adam of Bremen records that "rex Sueonum Hericus" invaded Denmark and expelled King Svend. He also records that King Erik was converted to Christianity and baptised in Denmark but may have relapsed into paganism on returning to Sweden.
According to Snorre, he died "in a sickbed at Uppsala 10 years after the death of Styrbjörn", and in another passage that his wife was a widow in 994. 1
According to the Hervarar saga, Björn Eriksson was the father of Olof (II) Björnsson and Eric the Victorious. Björn was purportedly the son of an Erik who fought Harald Fairhair and who succeeded the brothers Björn at Hauge and Anund Uppsale:
King Önund had a son called Erik, and he succeeded to the throne at Upsala after his father. He was a rich King. In his days Harold the Fair-haired made himself King of Norway. He was the first to unite the whole of that country under his sway. Erik at Upsala had a son called Björn, who came to the throne after his father and ruled for a long time. The sons of Björn, Eric the Victorious, and Olaf succeeded to the kingdom after their father. Olaf was the father of Styrbjörn the Strong.
Again according to the Hervarar saga, Anund (Old Norse: Önundr Uppsali), and his brother Björn succeeded king Erik Refilsson, their cousin. The two brothers shared the realm, so that Anund resided in Uppsala while Björn made his residence at Haugi ("the Barrow"). They are referred to as sons of Erik Björnsson, one of the sons of Björn Ironside, a semi-legendary king of Sweden. 2