In this work, we introduce and investigate the new concept of orthogonally quadratic \(s\) -functional equations where s is a non-zero fixed complex number with \(|s|<1\) and orthogonally quadratic ternary \((h_{i})\) -hom-derivation on orthogonally ternary algebras. In particular, we solve orthogonally quadratic \(s\) -functional equation and show that it is a class of orthogonally quadratic mapping. Using the orthogonally fixed point theorem, we show that the orthogonally quadratic \(s\) -functional equation on orthogonally ternary algebras can be the stable Hyers-Ulam with Gǎvruta’s control function. Ultimately, we can demonstrate the Hyers-Ulam stability of orthogonally quadratic ternary \((h_{i})\) -hom-derivation with Gǎvruta’s control function.
