Research Article Orthogonally C ∗ -Ternary Jordan Homomorphisms and Jordan Derivations: Solution and Stability Vahid Keshavarz and Sedigheh Jahedi Department of Mathematics, Shiraz University of Technology, P.O. Box 71557•13876, Shiraz, Iran Correspondence should be addressed to Vahid Keshavarz; v.keshavarz68@yahoo.com Received 28 February 2022; Revised 23 April 2022; Accepted 12 December 2022; Published 26 December 2022 Academic Editor: Li Guo Copyright © 2022 Vahid Keshavarz and Sedigheh Jahedi. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this work, by using some orthogonally fxed 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. 1. Introduction and Preliminaries A classical question in the sense of a functional equation says that “when is it true that a function which approximately satisfes a functional equation must be close to an exact solution of the equation?” lam [1] raised the question of stability of functional equations and Hyers [2] was the frst to give an afrmative answer to the question of lam for additive mapping between Banach spaces. In 1987, Rassias [3] proved a generalized version of the Hyers’ theorem for approximately additive maps. Te study of stability problem of functional equations have been done by several authors on diferent spaces such as Banach, C ∗ •Banach algebras and modular spaces (for example see [4–13]). One of the stimulating aspects is to examine the stability of those functional equations whose general solutions exist and are useful in characterizing entropies [14]. Recently, Eshaghi Gordji et al. [15] introduced the no• tion of the orthogonal set, which contains the notion of orthogonality in normed space. Te study on orthogonal sets has been done by several authors (for example, see [16–18]) Defnition 1 (see [15]). Let X ≠∅ and ⊥⊆X × X be a binary relation. If there exists x 0 ∈ X such that for all y ∈ X, y⊥x 0 or x 0 ⊥y. (1) Ten ⊥ is called an orthogonally set (briefy O•set). We denote this O•set by (X, ⊥). Let (X, ⊥) beanO•setand (X, d) be a generalized metric space, then (X, ⊥,d) is called orthogonally generalized metric space. Let (X, ⊥,d) be an orthogonally metric space. (i) A sequence x n  n∈N is called orthogonally sequence (briefy O•sequence) if for any n ∈ N, x n ⊥x n+1 or x n+1 ⊥x n . (2) (ii) Mapping f: X ⟶ X is called ⊥− continuous in x ∈ X if for each O•sequence x n  n∈N in X with x n ⟶ x, then f(x n ) ⟶ f(x). Clearly, every continuous map is ⊥− continuous at any x ∈ X. Hindawi Journal of Mathematics Volume 2022, Article ID 3482254, 7 pages https://doi.org/10.1155/2022/3482254