In Greek mythology, Libya (Libye) daughter of Epaphus and Memphis is the eponym of the land of Libya. By Poseidon she is mother of Belus and Agenor, the twin founders of the Egyptian and Phoenician royal stems that lead to Danaus, Aegyptus, Europa, and Cadmus. A rarer Oceanid Libya (daughter of Oceanus and Pompholyge) is a different figure.
Adapted from Wikipedia, "Libya (mythology)" · CC BY-SA 4.0
I.Eponym and mother of twins
As daughter of Epaphus (Io's son) and Memphis, Libya stands at the hinge between the Argive Io-line and the Mediterranean foundation myths. Poseidon fathers on her Belus, who stays to rule Egypt, and Agenor, who holds the Phoenician coast — the pair from whom Danaus, Aegyptus, Europa, Cadmus, and their houses descend in the common stemma.
Some sources also make her mother of Lamia. The ancient ethnographic name of North Africa west of Egypt was explained from this heroine.
II.Homonym
A separate Libya, daughter of Oceanus and Pompholyge and sister of Asia, appears in Andron and related notices as Triton's consort and mother of nymphs. The atlas id libya is the Epaphid eponym and mother of Belus and Agenor.