These verses are traditionally chanted before chanting the Viṣṇu Sahasranāma. As we go along, I will try to fill in few details of the great sages mentioned in these verses.
व्यासं वसिष्ठनप्तारं शक्तेः पौत्रमकल्मषम् ।
पराशरात्मजं वन्दे शुकतातं तपोनिधिम् ॥
I salute Sage Vyāsa, the great grandson of Sage Vasiṣṭha and the grandson of Sage Śakti, the son of Parāśara and the father of Sage Śuka, and who is by himself an abode of austerity and who is free of all blemishes.
Sage Vyāsa refers to Sage Veda Vyāsa, who is the legendary complier of the four Vedās, the author of the Purānās and the Māhābhārata. The festival of Guru Pūrṇima which is also known as Vyāsa Pūrṇima is dedicated to him.
Sage Vasiṣṭha the great-grandfather of Sage Vyāsa, is highly revered in Sanatana Dharma. He was one of the sons (mānas-putra) of Lord Brahma.
Sage Śakti was a revered Vedic rishi, the eldest son of Sage Vasiśṭha and Arundhati, and the father of Sage Parāśara. Known for his profound knowledge, he was a key figure in the lineage of sages mentioned in the Mahābhārata and Purāṇas.
Sage Parāśara is a revered Vedic sage, recognized as the author of the Viṣṇu Purāṇa, the foundational Brhat Parāshara Hora Śāstra (Vedic astrology), and a Smr̥ti text. He is the grandson of Sage Vasiśṭha, son of Sage Śaktii, and the father of Sage Vyāsa.
व्यासाय विष्णुरूपाय व्यासरूपाय विष्णवे ।
नमो वै ब्रह्मनिधये वासिष्ठाय नमो नमः ॥ ४॥
Salutations to Vyāsa who is in the form of Viṣṇu and salutations to Viṣṇu who is in the form of Vyāsa. Salutations again and again to him, who is an abode of the Vedas and who is of the lineage of Vasiṣṭha.
अविकाराय शुद्धाय नित्याय परमात्मने ।
सदैकरूपरूपाय विष्णवे सर्वजिष्णवे ॥ ५॥
(Prostrations) to Lord Viṣṇu, who is the Supreme Lord, changeless, pure, timeless, always of the same nature and ever victorious.
यस्य स्मरणमात्रेण जन्मसंसारबन्धनात् ।
विमुच्यते नमस्तस्मै विष्णवे प्रभविष्णवे ॥ ६॥
Salutations to Lord Viṣṇu, who is almighty and by remembering whom, one is freed from the cycle of birth and death.
