## Jordan *-derivations on $$C^*$$-algebras and $$JC^*$$-algebras.(English)Zbl 1243.46046

Summary: We investigate Jordan *-derivations on $$C^*$$-algebras and Jordan *-derivations on $$JC^*$$-algebras associated with the following functional inequality $$\| f(x)+f(y)+kf(z)\| \leq \| kf((x+y)/k+z)\|$$ for some integer $$k$$ greater than 1. We moreover prove the generalized Hyers-Ulam stability of Jordan *-derivations on $$C^*$$-algebras and of Jordan *-derivations on $$JC^*$$-algebras associated with the following functional equation $$f((x+y)/k+z)=(f(x)+f(y))/k+f(z)$$ for some integer $$k$$ greater than 1.

### MSC:

 46L05 General theory of $$C^*$$-algebras 46L70 Nonassociative selfadjoint operator algebras 39B82 Stability, separation, extension, and related topics for functional equations 47B47 Commutators, derivations, elementary operators, etc.
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