‎let $mathcal{a}$ be a unital banach algebra‎, ‎$mathcal{m}$ be a left $mathcal{a}$-module‎, ‎and $w$ in $mathcal{z}(mathcal{a})$ be a left separating point of $mathcal{m}$‎. ‎we show that if $mathcal{m}$ is a unital left $mathcal{a}$-module and $delta$ is a linear mapping from $mathcal{a}$ into $mathcal{m}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a jordan left de...

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

An inference graph can have many \deriva-tion strategies", each a particular ordering of the steps involved in reducing a given query to a sequence of database retrievals. An \optimal strategy" for a given distribution of queries is a complete strategy whose \expected cost" is minimal, where the expected cost depends on the conditional probabilities that each requested retrieval succeeds , give...

In this paper, we establish the generalized Hyers-Ulam stability of Jordan homomorphisms and Jordan derivations between ternary algebras via the generalized Jensen equation rf( sx+ty r ) = sf(x) + tf(y).

Let $R$ be a 2-torsion free ring and $U$ be a square closed Lie ideal of $R$. Suppose that $alpha, beta$ are automorphisms of $R$. An additive mapping $delta: R longrightarrow R$ is said to be a Jordan left $(alpha,beta)$-derivation of $R$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin R$. In this paper it is established that if $R$ admits an additive mapping $G : Rlongrigh...