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In this paper we introduce an analog of the (classical) Yang-Baxter equation(CYBE) for vertex operator algebras (VOAs) in its tensor form, called thevertex operator Yang-Baxter equation (VOYBE). When specialized to level one ofa vertex operator algebra, the VOYBE reduces to the CYBE for Lie algebras. Togive an operator form of the VOYBE, we also introduce the notion of relativeRota-Baxter operators (RBOs) as the VOA analog of relative RBOs (classicallycalled $\mathcal{O}$-operators) for Lie algebras. It is shown thatskewsymmetric solutions $r$ to the VOYBE in a VOA $U$ are characterized by thecondition that their corresponding linear maps $T_r:U'\to U$ from the gradeddual $U'$ of $U$ are relative RBOs. On the other hand, strong relative RBOs ona VOA $V$ associated to an ordinary $V$-module $W$ are characterized by thecondition that their antisymmetrizers are solutions to the $0$-VOYBE in thesemidirect product VOA $V\rtimes W'$. Specializing to the first level of a VOA,these relations between the solutions of the VOYBE and the relative RBOs forVOAs recover the classical relations between the solutions of the CYBE and therelative RBOs for Lie algebras.

Classical Yang-Baxter equation for vertex operator algebras and its operator forms