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The intensive study of Rota-Baxter operators on the polynomial algebra $F[x]$has been started with the work of S.H. Zheng, L. Guo, and M. Rosenkranz (2015).We deal with the case of two variables and monomial Rota-Baxter operators ofnonzero weight. The family of such operators arisen from homomorphic averagingoperators on $F[x,y]$ is described.

Monomial Rota-Baxter operators of nonzero weight on $F[x,y]$ coming from averaging operators