Using the Hyers-Ulam-Rassias stability method, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphismsin Banach algebras and of derivations on Banach ...

‎let $x$‎, ‎$y$ and $z$ be banach spaces and $f:xtimes y‎ ‎longrightarrow z$ a bounded bilinear map‎. ‎in this paper we‎ ‎study the relation between arens regularity of $f$ and the‎ ‎reflexivity of $y$‎. ‎we also give some conditions under which the‎ ‎arens regularity of a banach algebra $a$ implies the arens‎ ‎regularity of certain banach right module action of $a$‎ .

this paper continues the investigation of the rst author begun in part one. the hereditary properties of n-homomorphism amenability for banach algebras are investigated and the relations between n-homomorphism amenability of a banach algebra and its ide- als are found. analogous to the character amenability, it is shown that the tensor product of two unital banach algebras is n-homomorphism am...

In this article, the notion of $n-$derivation is introduced for all integers $ngeq 2$. Although all derivations are $n-$derivations,  in general these notions are not equivalent. Some properties of ordinary derivations are  investigated for $n-$derivations. Also, we show that under certain mild condition  $n-$derivations are derivations.

Ideal Connes-amenability of dual Banach algebras was investigated in [17] by A. Minapoor, A. Bodaghi and D. Ebrahimi Bagha. They studied weak∗continuous derivations from dual Banach algebras into their weak∗-closed two- sided ideals. This work considers weak∗-continuous derivations of dual triangular Banach algebras into their weak∗-closed two- sided ideals . We investigate when weak∗continuous...

Let A be an algebra over the real or complex field F. An additive mapping d : A → A is said to be a left derivation resp., derivation if the functional equation d xy xd y yd x resp., d xy xd y d x y holds for all x, y ∈ A. Furthermore, if the functional equation d λx λd x is valid for all λ ∈ F and all x ∈ A, then d is a linear left derivation resp., linear derivation . An additive mapping G : ...

Let A and B be centrally closed prime complex Banach algebras with linear involution. If A is semisimple, then any Lie derivation of the skew elements of A is continuous and any Lie isomorphism from the skew elements of B onto the skew elements of A is continuous. The Lie product [a, b] = ab−ba induces on any Banach algebra A a Lie structure of great interest for their intimate connections with...

Let B be a complex unital Banach algebra. We consider the Banach algebra A = B × C ordered by the algebra cone K = {(a, ξ) ∈ A : ‖a‖ ≤ ξ}, and investigate the connection between results on ordered Banach algebras and the right bound of the numerical range of elements in B. 1. Ordered Banach algebras The aim of this paper is to stress the aspect of the applicability of the ordered Banach algebra...

this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...