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

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