In this article, weintroduce 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.
On the Stability of Quartic Functional Equations via Fixed Point and Direct Method
