Weak right η -centralizers of prime rings

This work encompasses the study of certain weak maps termed as weak right η-centralizers defined on D a noncommutative prime ring to Qml(D). The first section provides an overview of the motivation behind our work. In the second section, our main focus is to establish the characterization of weak right η-centralizers while addressing the theory of functional identities, particularly in the challenging case of low dimensions. Furthermore, in the third section, we derive the characterization of weak Jordan σ-derivations based on the aforementioned characterization.