Isomorphisms in unital $C^*$-algebras
C.
Park
Department of Mathematics, Hanyang University,
Seoul 133-791, Republic of Korea
author
Th. M.
Rassias
Department of Mathematics,
National Technical
University of Athens,
Zografou Campus, 15780 Athens, Greece
author
text
article
2010
eng
It is shown that every almost linear bijection $h : A\rightarrow B$ of a unital $C^*$-algebra $A$ onto a unital $C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for all unitaries $u \in A$, all $y \in A$, and all $n\in \mathbb Z$, and that almost linear continuous bijection $h : A \rightarrow B$ of a unital $C^*$-algebra $A$ of real rank zero onto a unital $C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for all $u \in \{ v \in A \mid v = v^*, \|v\|=1, v \text{ is invertible} \}$, all $y \in A$, and all $n\in \mathbb Z$. Assume that $X$ and $Y$ are left normed modules over a unital $C^*$-algebra $A$. It is shown that every surjective isometry $T : X \rightarrow Y$, satisfying $T(0) =0$ and $T(ux) = u T(x)$ for all $x \in X$ and all unitaries $u \in A$, is an $A$-linear isomorphism. This is applied to investigate $C^*$-algebra isomorphisms in unital $C^*$-algebras.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
1
v.
2
no.
2010
1
10
https://ijnaa.semnan.ac.ir/article_62_c9da465ab255a2d53f17b3a6cdf00d84.pdf
dx.doi.org/10.22075/ijnaa.2010.62
A new method for the generalized Hyers-Ulam-Rassias stability
P.
Gavruta
Department of Mathematics,
University "Politehnica" of Timisoara, 300006, Timisoara, Romania
author
L.
Gavruta
Department of Mathematics,
University "Politehnica" of Timisoara, 300006, Timisoara, Romania
author
text
article
2010
eng
We propose a new method, called the weighted space method, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
1
v.
2
no.
2010
11
18
https://ijnaa.semnan.ac.ir/article_70_53c5dcd77c8d0bb23122772e4b5b6a97.pdf
dx.doi.org/10.22075/ijnaa.2010.70
Hyers-Ulam stability of Volterra integral equation
M.
Gachpazan
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran.
author
O.
Baghani
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran.
author
text
article
2010
eng
We will apply the successive approximation method for proving the Hyers--Ulam stability of a linear integral equation of the second kind.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
1
v.
2
no.
2010
19
25
https://ijnaa.semnan.ac.ir/article_71_d9b6a3c6b2cef34d8b142ca405cf0387.pdf
dx.doi.org/10.22075/ijnaa.2010.71
stability of the quadratic functional equation
E.
Elqorachi
Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco
author
Y.
Manar
Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco
author
Th. M.
Rassias
Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece
author
text
article
2010
eng
In the present paper a solution of the generalized quadratic functional equation$$f(kx+ y)+f(kx+\sigma(y))=2k^{2}f(x)+2f(y),\phantom{+} x,y\in{E}$$
is given where $\sigma$ is an involution of the normed space $E$ and $k$ is a fixed positive integer. Furthermore we investigate the Hyers-Ulam-Rassias stability of the functional equation. The Hyers-Ulam stability on unbounded domains is also studied. Applications of the results for the asymptotic behavior of the generalized quadratic functional equation are provided.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
1
v.
2
no.
2010
26
35
https://ijnaa.semnan.ac.ir/article_72_80bd73337686e609bb56f0fac56e6130.pdf
dx.doi.org/10.22075/ijnaa.2010.72
Approximately higher Hilbert $C^*$-module derivations
M. B.
Ghaemi
Department of Mathematics, Iran
University of Science and Technology, Tehran, Iran
author
B.
Alizadeh
PhD and Graduate Center, Payame Noor University,
Shahnaz Alley Haj Mahmood Norian Street, Shiraz, Iran
author
text
article
2010
eng
We show that higher derivations on a Hilbert $C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
1
v.
2
no.
2010
36
43
https://ijnaa.semnan.ac.ir/article_73_fee714a36aebab5998d94504bea16488.pdf
dx.doi.org/10.22075/ijnaa.2010.73
Fuzzy approximately additive mappings
H.
Khodaei
Department of Mathematics,
Semnan University P. O. Box 35195-363, Semnan, Iran.
author
M.
Kamyar
Department of Mathematics,
Semnan University P. O. Box 35195-363, Semnan, Iran.
author
text
article
2010
eng
Moslehian and Mirmostafaee, investigated the fuzzy stability problems for the Cauchy additive functional equation, the Jensen additive functional equation and the cubic functional equation in fuzzy Banach spaces. In this paper, we investigate the generalized Hyers–-Ulam--Rassias stability of the generalized additive functional equation with $n$--variables, in fuzzy Banach spaces. Also, we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost additive function, control function and the unique additive function which approximate the almost additive function.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
1
v.
2
no.
2010
44
53
https://ijnaa.semnan.ac.ir/article_74_03299cf23773f3e7dad90060197c6926.pdf
dx.doi.org/10.22075/ijnaa.2010.74
Generalized additive functional inequalities in Banach algebras
C.
Park
Department of Mathematics, Hanyang University,
Seoul 133-791, Republic of Korea
author
A.
Najati
Faculty of Sciences, Department of Mathematics,
University of Mohaghegh Ardabili,
Ardabil,
Islamic Republic of Iran.
author
text
article
2010
eng
Using the Hyers-Ulam-Rassias stability method, we investigate isomorphisms in Banach algebras and derivations on Banach algebras associated with the following generalized additive functional inequality\begin{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 homomorphism in Banach algebras and of derivations on Banach algebras associated with the generalized additive functional inequality (0.1).
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
1
v.
2
no.
2010
54
62
https://ijnaa.semnan.ac.ir/article_75_d483822afcaa756db55cc195d4bd784d.pdf
dx.doi.org/10.22075/ijnaa.2010.75
Lie $^*$-double derivations on Lie $C^*$-algebras
N.
Ghobadipour
Department of Mathematics,
Urmia University, Urmia, Iran.
author
text
article
2010
eng
A unital $C^*$-algebra $\mathcal{A}$ endowed with the Lie product $[x,y]=xy- yx$ on $\mathcal{A}$ is called a Lie $C^*$-algebra. Let $\mathcal{A}$ be a Lie $C^*$-algebra and $g,h:\mathcal{A}\to \mathcal{A}$ be $\mathbb{C}$-linear mappings. A $\mathbb{C}$-linear mapping $f:\mathcal{A}\to \mathcal{A}$ is called a Lie $(g,h)$--double derivation if $f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all $a,b\in \mathcal{A}$. In this paper, our main purpose is to prove the generalized Hyers–Ulam–Rassias stability of Lie $*$-double derivations on Lie $C^*$-algebras associated with thefollowing additive mapping:$$\sum^{n}_{k=2}(\sum^{k}_{i_{1}=2} \sum^{k+1}_{i_{2}=i_{1}+1}...\sum^{n}_{i_{n-k+1}=i_{n-k}+1}) f(\sum^{n}_{i=1, i\neqi_{1},..,i_{n-k+1} } x_{i}-\sum^{n-k+1}_{ r=1}x_{i_{r}})+f(\sum^{n}_{ i=1} x_{i})=2^{n-1} f(x_{1})$$ for a fixed positive integer $n$ with $n \geq 2.$
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
1
v.
2
no.
2010
63
71
https://ijnaa.semnan.ac.ir/article_76_53a185511f0f7605fd4bc2aa5437e49a.pdf
dx.doi.org/10.22075/ijnaa.2010.76
Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces
S.
Shakeri
Department of Mathematics,
Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran
author
R.
Saadati
Department of Mathematics,
Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran
author
C.
Park
Department of Mathematics, Research Institute for Natural Sciences, Hanyang University,
Seoul 133-791, Korea
author
text
article
2010
eng
In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functional equation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $\mathcal{L}$-fuzzy normed spaces.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
1
v.
2
no.
2010
72
83
https://ijnaa.semnan.ac.ir/article_77_f653e0485a7b895e88a5a8030a62f80c.pdf
dx.doi.org/10.22075/ijnaa.2010.77
Stability of generalized QCA-functional equation in P-Banach spaces
S.
Zolfaghari
Department of Mathematics,
Urmia University, Urmia, Iran.
author
text
article
2010
eng
In this paper, we investigate the generalized Hyers-Ulam-Rassias stability for the quartic, cubic and additive functional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k \in \mathbb{Z}-{0,\pm1}$) in $p-$Banach spaces.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
1
v.
2
no.
2010
84
99
https://ijnaa.semnan.ac.ir/article_78_f302ba7732cdf643ccca509d52760006.pdf
dx.doi.org/10.22075/ijnaa.2010.78
Intuitionistic fuzzy stability of a quadratic and quartic functional equation
S.
Abbaszadeh
Department of Mathematics, Semnan
University, P. O. Box 35195-363,
Semnan, Iran.
author
text
article
2010
eng
In this paper, we prove the generalized Hyers--Ulam stability of a quadratic and quartic functional equation in intuitionistic fuzzy Banach spaces.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
1
v.
2
no.
2010
100
124
https://ijnaa.semnan.ac.ir/article_79_0f500f465e1383e760d9492604334fca.pdf
dx.doi.org/10.22075/ijnaa.2010.79