Let D be a mapping from an alternative ring R into itself satisfyingUnder some conditions on R, we show that D is additive.

The purpose of this note is to prove the following. Suppose $\mathfrak{R}$ is a semiprime unity ring having an idempotent element $e$ ($e\neq 0,~e\neq 1$) which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on $\mathfrak{R}$ is a generalized derivation.

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Let [Formula: see text] and [Formula: see text] be two ∗-Jordan algebras with identities [Formula: see text] and [Formula: see text], respectively, and [Formula: see text] a nontrivial ∗-idempotent in [Formula: see text]. In this paper, we study the characterization of multiplicative ∗-Jordan-type maps. In particular, we provide a characterization in the case of unital prime associative algebra endowed with an involution.

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