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The concepts of (generalized) (θ,φ)-prederivations and (generalized) Jordan (θ,φ)-prederivations on a Lie superalgebra are introduced. It is proved that Jordan (θ,φ)-prederivations (resp., generalized Jordan (θ,φ)-prederivations) are (θ,φ)-prederivations (resp., generalized (θ,φ)-prederivations) on a Lie superalgebra under some conditions. In particular, Jordan θ-prederivations are θ-prederivations on a Lie superalgebra.

On Generalized Jordan Prederivations and Generalized Prederivations of Lie Superalgebras