using fixed pointmethods, we investigate approximately higher ternary jordan derivations in banach ternaty algebras via the cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$

Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. Given two derivations $delta$ and $delta'$ on a $C^*$-algebra $mathfrak A$, we prove that there exists a derivation $Delta$ on $mathfrak A$ such that $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdel...

Let $R$ be a ring and $Z(R)$ the center of $R.$ The aim this paper is to define notions centrally extended Jordan derivations $\ast$-derivations, prove some results involving these mappings. Precisely, we that if $2$-torsion free noncommutative prime admits derivation (resp. $\ast$-derivation) $\delta:R\to R$ such that\[[\delta(x),x]\in Z(R)~~(resp.~~[\delta(x),x^{\ast}]\in Z(R))\text{ for all ...

Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.

begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}

let $mathfrak{a}$ be an algebra. a linear mapping $delta:mathfrak{a}tomathfrak{a}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{a}$. given two derivations $delta$ and $delta'$ on a $c^*$-algebra $mathfrak a$, we prove that there exists a derivation $delta$ on $mathfrak a$ such that $deltadelta'=delta^2$ if and only if either $delta'=0$...