On $\theta$-centralizing $\theta$-generalized derivations on convolution algebras

Let $\theta$ be an isomorphism on $L_0^{\mathrm{\infty }}(w{)}^{\ast }$. In this paper, we investigate $\theta$-generalized derivations on $L_0^{\mathrm{\infty }}(w{)}^{\ast }$. We show that every $\theta$-centralizing $\theta$-generalized derivation on $L_0^{\mathrm{\infty }}(w{)}^{\ast }$ is a $\theta$-right centralizer. We also prove that this result is true for $\theta$-skew centralizing $\theta$-generalized derivations.