In this work, by using some orthogonally fixed point theorem, we prove the stability and hyperstability of orthogonally
C
∗
-ternary Jordan homomorphisms between
C
∗
-ternary Banach algebras and orthogonally
C
∗
-ternary Jordan derivations of some functional equation on
C
∗
-ternary Banach algebras.
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