ORIGINAL_ARTICLE
Isomorphisms in unital $C^*$-algebras
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.
https://ijnaa.semnan.ac.ir/article_62_c9da465ab255a2d53f17b3a6cdf00d84.pdf
2010-06-01
1
10
10.22075/ijnaa.2010.62
generalized Hyers-Ulam stability
$C^*$-algebra isomorphism
real rank zero
isometry
C.
Park
1
Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea
LEAD_AUTHOR
Th. M.
Rassias
2
Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece
AUTHOR
ORIGINAL_ARTICLE
A new method for the generalized Hyers-Ulam-Rassias stability
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.
https://ijnaa.semnan.ac.ir/article_70_53c5dcd77c8d0bb23122772e4b5b6a97.pdf
2010-06-01
11
18
10.22075/ijnaa.2010.70
Hyers–-Ulam--Rassias stability
functional equation
Volterra integral operator
Fredholm integral operator
Weighted space method
P.
Gavruta
1
Department of Mathematics, University "Politehnica" of Timisoara, 300006, Timisoara, Romania
LEAD_AUTHOR
L.
Gavruta
2
Department of Mathematics, University "Politehnica" of Timisoara, 300006, Timisoara, Romania
AUTHOR
ORIGINAL_ARTICLE
Hyers-Ulam stability of Volterra integral equation
We will apply the successive approximation method for proving the Hyers--Ulam stability of a linear integral equation of the second kind.
https://ijnaa.semnan.ac.ir/article_71_d9b6a3c6b2cef34d8b142ca405cf0387.pdf
2010-06-01
19
25
10.22075/ijnaa.2010.71
Hyers--Ulam stability
Banach's fixed point theorem
Volterra integral equation
Successive approximation method
M.
Gachpazan
1
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
AUTHOR
O.
Baghani
2
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
LEAD_AUTHOR
ORIGINAL_ARTICLE
stability of the quadratic functional equation
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.
https://ijnaa.semnan.ac.ir/article_72_80bd73337686e609bb56f0fac56e6130.pdf
2010-06-01
26
35
10.22075/ijnaa.2010.72
Hyers-Ulam-Rassias stability
quadratic functional equation
E.
Elqorachi
1
Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco
LEAD_AUTHOR
Y.
Manar
2
Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco
AUTHOR
Th. M.
Rassias
3
Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece
AUTHOR
ORIGINAL_ARTICLE
Approximately higher Hilbert $C^*$-module derivations
We show that higher derivations on a Hilbert $C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.
https://ijnaa.semnan.ac.ir/article_73_fee714a36aebab5998d94504bea16488.pdf
2010-06-01
36
43
10.22075/ijnaa.2010.73
Hyers--Ulam stability
Hilbert $C^{*}-$modules
Derivation
Higher derivation
Fixed point theorem
M. B.
Ghaemi
1
Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
AUTHOR
B.
Alizadeh
2
PhD and Graduate Center, Payame Noor University, Shahnaz Alley Haj Mahmood Norian Street, Shiraz, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Fuzzy approximately additive mappings
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.
https://ijnaa.semnan.ac.ir/article_74_03299cf23773f3e7dad90060197c6926.pdf
2010-06-01
44
53
10.22075/ijnaa.2010.74
Fuzzy stability
Additive functional equation
Fuzzy normed space
H.
Khodaei
1
Department of Mathematics, Semnan University P. O. Box 35195-363, Semnan, Iran.
LEAD_AUTHOR
M.
Kamyar
2
Department of Mathematics, Semnan University P. O. Box 35195-363, Semnan, Iran.
AUTHOR
ORIGINAL_ARTICLE
Generalized additive functional inequalities in Banach algebras
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).
https://ijnaa.semnan.ac.ir/article_75_d483822afcaa756db55cc195d4bd784d.pdf
2010-06-01
54
62
10.22075/ijnaa.2010.75
Hyers-Ulam-Rassias stability
generalized additive functional inequality
algebra homomorphism in Banach algebra
derivation on Banach algebra
C.
Park
1
Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea
LEAD_AUTHOR
A.
Najati
2
Faculty of Sciences, Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Islamic Republic of Iran.
AUTHOR
ORIGINAL_ARTICLE
Lie $^*$-double derivations on Lie $C^*$-algebras
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 $n \geq 2.$
https://ijnaa.semnan.ac.ir/article_76_53a185511f0f7605fd4bc2aa5437e49a.pdf
2010-06-01
63
71
10.22075/ijnaa.2010.76
Generalized Hyers-Ulam-Rassias stability
$*$-double derivation
Lie $C^*$-algebra
N.
Ghobadipour
1
Department of Mathematics, Urmia University, Urmia, Iran.
LEAD_AUTHOR
ORIGINAL_ARTICLE
Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces
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.
https://ijnaa.semnan.ac.ir/article_77_f653e0485a7b895e88a5a8030a62f80c.pdf
2010-06-01
72
83
10.22075/ijnaa.2010.77
$mathcal{L}$-fuzzy metric and normed spaces
intuitionistic fuzzy metric and normed spaces
generalized Hyers-Ulam stability
quadratic functional equation
non-Archimedean $mathcal{L}$-fuzzy normed space
S.
Shakeri
1
Department of Mathematics, Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran
AUTHOR
R.
Saadati
2
Department of Mathematics, Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran
AUTHOR
C.
Park
3
Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea
LEAD_AUTHOR
ORIGINAL_ARTICLE
Stability of generalized QCA-functional equation in P-Banach spaces
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.
https://ijnaa.semnan.ac.ir/article_78_f302ba7732cdf643ccca509d52760006.pdf
2010-06-01
84
99
10.22075/ijnaa.2010.78
stability
QCA-functional equation
$p-$Banach space
S.
Zolfaghari
1
Department of Mathematics, Urmia University, Urmia, Iran.
LEAD_AUTHOR
ORIGINAL_ARTICLE
Intuitionistic fuzzy stability of a quadratic and quartic functional equation
In this paper, we prove the generalized Hyers--Ulam stability of a quadratic and quartic functional equation in intuitionistic fuzzy Banach spaces.
https://ijnaa.semnan.ac.ir/article_79_0f500f465e1383e760d9492604334fca.pdf
2010-06-01
100
124
10.22075/ijnaa.2010.79
Intuitionistic fuzzy normed space
Mixed functional equation
Intuitionistic fuzzy stability
S.
Abbaszadeh
1
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
LEAD_AUTHOR