In this paper, we present a Hyers–Ulam stability result for the approximately linear recurrence in Banach spaces. An example is given to show the results in more tangible form.
We apply a fixed point theorem to prove that there exists a unique derivation close to an approximately generalized derivation in Lie C*-algebras. Also, we prove the hyperstability of generalized derivations. In other words, we find some conditions under which an approximately generalized derivation becomes a derivation.
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