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In this article, we introduce a kind of binary relation on a nonempty set with name of orthogonally relation which we develop for sequences, continuous maps, metric spaces, contraction maps, preserving maps and etc. All of the above concepts are generalized forms of ordinary case, so they are very important for extension and finding new results. we expect some of the concepts in the mathematics can be changed by orthogonally relation, such as functional equations and some of the theorem in the fixed point theorem method. In this research we illustrate one of the applications of orthogonally relation on ternary cubic homomorphism and ternary cubic derivations, so we prove the stability of orthogonally ternary cubic homomorphisms and orthogonally ternary cubic derivations on C∗-ternary algebras for the functional equation by using fixed point method. Also to create the stability, we choose a suitable control function and we show ability and validity of the proposed method for the functional analysis.

Introducing of an orthogonally relation for stability of ternary cubic homomorphisms and derivations on C*-ternary algebras