As you can see from the attached extract of the Sanskrit Introduction to the 1864 pothi print edition of Veṅkaṭādhvarin's Lakṣmīsahasra, evidently, while the great Appayya Dīkṣita was mainly a Śaiva Advaitin vehemently attacking especially the Mādhva Vaiṣṇavas in his Madhvatantramukhamardana, his son Raghunātha Dīkṣita and grandson Veṅkaṭādhvarin were Vaiṣṇavas.  Among his later descendants we have Śaiva scholars like Nīlakaṇṭha Dīkṣita.  How did these Śaiva and Vaiṣṇava affiliations develop within this one and the same family?  If anyone knows sources for the family history of Appayya Dīkṣita and his lineage, I would very much appreciate to know those sources.  Thanks for your assistance.

Madhav M. Deshpande

Ann Arbor, Michigan, USA