we investigate the stability of generalizedderivations on banach algebras with a bounded central approximateidentity. we show that every approximate generalized derivation inthe sense of rassias, is an exact generalized derivation. also thestability problem of generalized derivations on the faithful banachalgebras is investigated.

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 $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

background: early diagnosis of left ventricular mass (lvm) inappropriateness and left ventricular hypertrophy   (lvh) can result in preventing diastolic left ventricular dysfunction and its related morbidity and mortality. this study was performed to determine if diastolic dysfunction   is associated with lvh and inappropriate lvm. methods: one hundred   and twenty five uncomplicated hypertensi...

recently, the algebraic theory of mv -algebras is intensively studied. in this paper, we extend the concept of derivation of $mv$-algebras and we give someillustrative examples. moreover, as a generalization of derivations of $mv$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $mv$-algebras.also, we investigate some properties of them.

This paper constructs presentations via finite complete rewriting systems for Plactic monoids of types An, Bn, Cn, Dn, and G2, using a unified proof strategy that depends on Kashiwara’s crystal bases and analogies of Young tableaux, and on Lecouvey’s presentations for these monoids. As corollaries, we deduce that Plactic monoids of these types have finite derivation type and satisfy the homolog...

Patients: Patients ≥ 30 years of age (derivation group, n = 33 268, median age 52 y, 62% men; validation group, n = 5821, median age 55 y, 55% men) with normal ECGs and suspected CAD referred for symptom-limited exercise treadmill testing. Exclusion criteria were coronary disease, heart failure, left ventricular systolic dysfunction, cardiomyopathy, valvular or congenital heart disease, past re...

This paper is a study of derivations on unbounded operator algebras in connection with those in operator algebras. In particular we study spatiality of derivations in several situations. We give the characterization of derivations on general «-algebras by using positive linear functionals. We also show that a derivation with some range-property on a left ■EW*-algebra induced by an unbounded Hub...