On Higher-splitting methods of associative conformal algebras

In the present work, we study higher-splitting methods in associative conformal algebras and introduce Dyck m conformal algebras as a natural generalization of known splitting structures. It is shown that any (α, β)-weighted Rota-Baxter operator on an associative conformal algebra induces a Dyck m conformal algebra. We further define Rota m conformal algebras and establish their correspondence with homomorphic averaging operators, clarifying their role within the higher-splitting concept. Explicit constructions, examples, and functorial relations among these algebraic structures are provided.