Characterization of $ (\alpha, \beta) $ Jordan bi-derivations in prime rings

Abstract

<abstract><p>Let $ \mathfrak{S} $ be a prime ring with automorphisms $ \alpha, \beta $. A bi-additive map $ \mathfrak{D} $ is called an ($ \alpha, \beta $) Jordan bi-derivation if $ \mathfrak{D}(k^2, s) = \mathfrak{D}(k, s)\alpha(k) + \beta(k) \mathfrak{D}(k, s) $. In this paper, we find conditions under which a symmetric ($ \alpha, \beta $) Jordan bi-derivation becomes a symmetric ($ \alpha, \beta $) bi-derivation. We also characterize the symmetric $ (\alpha, \beta) $ Jordan bi-derivations.</p></abstract>