Characterization of \((\alpha ,\beta )\) biderivations in triangular algebras

In this paper we have define \((\alpha ,\beta )\) $(\alpha ,\beta )$ -biderivation on triangular algebra \(\mathcal {A}\) $\mathcal{A}$ and characterize some result on triangular algebras. Apart from that, in Theorem 3.5, we show that any map on \(\mathcal {A} \times \mathcal {A} \rightarrow \mathcal {A}\) $\mathcal{A}\times \mathcal{A}\to \mathcal{A}$ becomes \((\alpha ,\alpha )\) $(\alpha ,\alpha )$ -biderivation after imposing certain conditions.