Aśvapati(Aswapati) was the king of Madra. He did not have any child. To have a child, the king worshiped goddess Sāvitrī (Savitri). The goddess was pleased, and she blessed the king so that he could have a child. By the grace of goddess Sāvitrī, the king had a girl-child, who was named after the goddess.
When Sāvitrī grew up, the king Aśvapati was searching for a suitable man for his daughter. Hearing about the appearance and virtues of Satyvāna (Satyavana) from Nārada (Malati), he finally got her daughter married to Satyavān (Satyavana).
In Devībhāgavatapurāṇa (Devibhagavatapurana), the wife of Aśvapati was Mālatī (Malati). Mālatī was unable to become pregnancy, so Aśvapati, as per the advice of Vaśiṣṭha (Vasistha), worshiped goddess Sāvitrī. Even after performing tapasyā (tapasya; ascetic penance) at Puṣkaratīrtha (Pushkaratirtha), he did not have a vision of the goddess. He got a divine instruction to meditate upon the name of goddess Sāvitrī for ten millions of times. Maharṣi (Maharshi; great sage) Parāśara(Parasara) advised Aśvapati on the procedures of the worship, dhyāna (dhyana; meditation) of goddess Sāvitrī. Proceeding in this way, Aśvapati got a vision of the goddess, and got her blessings, too. Sāvitri gave him a boon that his desire for sons, and his wife’s desire for a daughter — both would be fruitful. In course of time, a daughter was born to Aśvapati, and she was named Sāvitrī.