scholarly journals Nearly generalized Jordan derivations

2011 ◽  
Vol 61 (1) ◽  
Author(s):  
M. Eshaghi Gordji ◽  
N. Ghobadipour

AbstractLet A be an algebra and let X be an A-bimodule. A ∂-linear mapping d: A → X is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ: A → X such that d(a 2) = ad(a)+δ(a)a for all a ∈ A. The main purpose of this paper is to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4311-4328
Author(s):  
A.R. Sharifi ◽  
Azadi Kenary ◽  
B. Yousefi ◽  
R. Soltani

The main goal of this paper is study of the Hyers-Ulam-Rassias stability (briefly HUR-approximation) of the following Euler-Lagrange type additive(briefly ELTA) functional equation ?nj=1f (1/2 ?1?i?n,i?j rixi- 1/2 rjxj) + ?ni=1 rif(xi)=nf (1/2 ?ni=1 rixi) where r1,..., rn ? R, ?ni=k rk?0, and ri,rj?0 for some 1? i < j ? n, in fuzzy normed spaces. The concept of HUR-approximation originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.


2009 ◽  
Vol 430 (5-6) ◽  
pp. 1479-1485 ◽  
Author(s):  
Jinchuan Hou ◽  
Xiaofei Qi

2009 ◽  
Vol 3 (1) ◽  
pp. 39-45 ◽  
Author(s):  
M. Frank ◽  
P. Găvruţa ◽  
M.S. Moslehian

We define the notion of ?-perturbation of a densely defined adjointable mapping and prove that any such mapping f between Hilbert A-modules over a fixed C*-algebra A with densely defined corresponding mapping g is A-linear and adjointable in the classical sense with adjoint g. If both f and g are every- where defined then they are bounded. Our work concerns with the concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias' stability theorem that appeared in his paper [On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300]. We also indicate complementary results in the case where the Hilbert C?-modules admit non-adjointable C*-linear mappings.


2021 ◽  
Vol 54 (1) ◽  
pp. 311-317
Author(s):  
Hadia Messaoudene ◽  
Nadia Mesbah

Abstract A new class of operators, larger than ∗ \ast -finite operators, named generalized ∗ \ast -finite operators and noted by Gℱ ∗ ( ℋ ) {{\mathcal{G {\mathcal F} }}}^{\ast }\left({\mathcal{ {\mathcal H} }}) is introduced, where: Gℱ ∗ ( ℋ ) = { ( A , B ) ∈ ℬ ( ℋ ) × ℬ ( ℋ ) : ∥ T A − B T ∗ − λ I ∥ ≥ ∣ λ ∣ , ∀ λ ∈ C , ∀ T ∈ ℬ ( ℋ ) } . {{\mathcal{G {\mathcal F} }}}^{\ast }\left({\mathcal{ {\mathcal H} }})=\{(A,B)\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\times {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}):\parallel TA-B{T}^{\ast }-\lambda I\parallel \ge | \lambda | ,\hspace{0.33em}\forall \lambda \in {\mathbb{C}},\hspace{0.33em}\forall T\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\}. Basic properties are given. Some examples are also presented.


Author(s):  
Ruth Nascimento Ferreira ◽  
Bruno Leonardo Macedo Ferreira

For a given ring $\Re$ and a locally finite pre-ordered set $(X, \leq)$, consider $I(X, \Re)$ to be the incidence algebra of $X$ over $\Re$. Motivated by a Xiao’s result which states that every Jordan derivation of $I(X, \Re)$ is a derivation in the case $\Re$ is 2-torsion free, one proves that each generalized Jordan derivation of $I(X, \Re)$ is a generalized derivation provided $\Re$ is 2-torsion free, getting as a consequence the above mentioned result.


2019 ◽  
Vol 109 (1) ◽  
pp. 36-43
Author(s):  
BRUNO L. M. FERREIRA ◽  
RUTH N. FERREIRA ◽  
HENRIQUE GUZZO

The purpose of this note is to prove the following. Suppose $\mathfrak{R}$ is a semiprime unity ring having an idempotent element $e$ ($e\neq 0,~e\neq 1$) which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on $\mathfrak{R}$ is a generalized derivation.


2014 ◽  
Vol 22 (1) ◽  
pp. 11-13 ◽  
Author(s):  
Nadeem ur Rehman ◽  
Abu Zaid Ansari ◽  
Tarannum Bano

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
A. Ebadian ◽  
S. Kaboli Gharetapeh ◽  
M. Eshaghi Gordji

Let , be two unital -algebras. We prove that every almost unital almost linear mapping : which satisfies for all , all , and all , is a Jordan homomorphism. Also, for a unital -algebra of real rank zero, every almost unital almost linear continuous mapping is a Jordan homomorphism when holds for all (), all , and all . Furthermore, we investigate the Hyers- Ulam-Aoki-Rassias stability of Jordan -homomorphisms between unital -algebras by using the fixed points methods.


2020 ◽  
Vol 17 (4) ◽  
pp. 426-437
Author(s):  
Nikolay N. Nosov

The article is devoted to L.I. Strakhovsky (alias Leonid Chatsky; 1898—1963), a Russian writer and poet of the first wave of emigration, and his poetry and prose reflected in foreign publications of his works in Russian. Returning to our culture the name of this author, now half-forgotten in his homeland, and introducing this name into literary studies, the article tries to reveal the thematic and stylistic diversity of L.I. Strakhovsky’s poetry and prose. The research’s object is foreign publications of L.I. Strakhovsky’s artistic works in separate books, almanacs and periodicals published in Belgium, Germany, Canada and identified through collection catalogues of leading Russian libraries (the Russian State library, the Alexander Solzhenitsyn House of Russia Abroad) and library resources that display foreign Russian-language publications by L.I. Strakhovsky. The article highlights and analyzes the main stylistic (symbolism, acmeism, “junior acmeism”) and thematic (autobiographical, English, mystical) components of L.I. Strakhovsky’s works, reveals the components’ individual features, the originality of their constancy and mutual influence. The main of these features is that L.I. Strakhovsky’s works can be stylistically periodized on the basis of the author’s increased propensity to cyclize his works though without creative evolution in the usual sense and with the stable nature of his working throughout his life. To review the publications and analyze the nature of L.I. Strakhovsky’s works, the article draws on the context of Russian and emigrant literature of his era, creatively associated with L.I. Strakhovsky and its main figures, and notes his literary and cultural influence.


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