Analysis of information sources in references of the Wikipedia article "Svayam Bhagavan" in English language version.
gavin flood."Early Vaishnava worship focuses on three deities who become fused together, namely Vasudeva-Krishna, Krishna-Gopala, and Narayana, who in turn all become identified with Vishnu. Put simply, Vasudeva-Krishna and Krishna-Gopala were worshiped by groups generally referred to as Bhagavatas, while Narayana was worshipped by the Pancaratra sect."
For his worshippers he is not an avatara in the usual sense, but Svayam Bhagavan, the Lord himself.p.109 Klaus Klostermaier translates it simply as "the Lord Himself"