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 allunitaries $u \in A$, all $y \in A$, and all $n\in \mathbb Z$, andthat almost linear continuous bijection $h : A \rightarrow B$ of aunital $C^*$-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
2010-06-01T11:23:20
2020-01-25T11:23:20
1
10
10.22075/ijnaa.2010.62
generalized Hyers-Ulam stability
$C^*$-algebra isomorphism
real rank zero
isometry
C.
Park
true
1
Department of Mathematics, Hanyang University,
Seoul 133-791, Republic of Korea
Department of Mathematics, Hanyang University,
Seoul 133-791, Republic of Korea
Department of Mathematics, Hanyang University,
Seoul 133-791, Republic of Korea
LEAD_AUTHOR
Th. M.
Rassias
true
2
Department of Mathematics,
National Technical
University of Athens,
Zografou Campus, 15780 Athens, Greece
Department of Mathematics,
National Technical
University of Athens,
Zografou Campus, 15780 Athens, Greece
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 \textit{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
2010-06-01T11:23:20
2020-01-25T11:23:20
11
18
10.22075/ijnaa.2010.70
Hyers–-Ulam--Rassias stability
functional equation
Volterra integral operator
Fredholm integral
operator
Weighted space method
P.
Gavruta
true
1
Department of Mathematics,
University "Politehnica" of Timisoara, 300006, Timisoara, Romania.
Department of Mathematics,
University "Politehnica" of Timisoara, 300006, Timisoara, Romania.
Department of Mathematics,
University "Politehnica" of Timisoara, 300006, Timisoara, Romania.
LEAD_AUTHOR
L.
Gavruta
true
2
Department of Mathematics,
University "Politehnica" of Timisoara, 300006, Timisoara, Romania.
Department of Mathematics,
University "Politehnica" of Timisoara, 300006, Timisoara, Romania.
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 forproving the Hyers--Ulam stability of a linear integral equation ofthe second kind.
https://ijnaa.semnan.ac.ir/article_71_d9b6a3c6b2cef34d8b142ca405cf0387.pdf
2010-06-01T11:23:20
2020-01-25T11:23:20
19
25
10.22075/ijnaa.2010.71
Hyers--Ulam stability
Banach's fixed
point theorem
Volterra integral equation
Successive approximation method
M.
Gachpazan
true
1
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran.
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran.
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran.
AUTHOR
O.
Baghani
true
2
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran.
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran.
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 generalizedquadratic functional equation$$f(kx+ y)+f(kx+\sigma(y))=2k^{2}f(x)+2f(y),\phantom{+} x,y\in{E}$$ isgiven where $\sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applications of the results for the asymptotic behavior of thegeneralized quadratic functional equation are provided.
https://ijnaa.semnan.ac.ir/article_72_80bd73337686e609bb56f0fac56e6130.pdf
2010-06-01T11:23:20
2020-01-25T11:23:20
26
35
10.22075/ijnaa.2010.72
Hyers-Ulam-Rassias stability
quadratic functional equation
E.
Elqorachi
true
1
Department of
Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir,
Morocco
Department of
Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir,
Morocco
Department of
Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir,
Morocco
LEAD_AUTHOR
Y.
Manar
true
2
Department of
Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir,
Morocco
Department of
Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir,
Morocco
Department of
Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir,
Morocco
AUTHOR
Th. M.
Rassias
true
3
Department of Mathematics, National
Technical University of Athens, Zografou Campus, 15780, Athens
Greece
Department of Mathematics, National
Technical University of Athens, Zografou Campus, 15780, Athens
Greece
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
2010-06-01T11:23:20
2020-01-25T11:23:20
36
43
10.22075/ijnaa.2010.73
Hyers--Ulam stability
Hilbert
$C^{*}-$modules
Derivation
Higher derivation
fixed point
theorem
M. B.
Ghaemi
true
1
Department of Mathematics, Iran
University of Science and Technology, Tehran, Iran
Department of Mathematics, Iran
University of Science and Technology, Tehran, Iran
Department of Mathematics, Iran
University of Science and Technology, Tehran, Iran
AUTHOR
B.
Alizadeh
true
2
PhD and Graduate Center, Payame Noor University,
Shahnaz Alley Haj Mahmood Norian Street,
$$AND$$
Tabriz College of
Technology, P. O. Box 51745-135, Tabriz, Iran.
PhD and Graduate Center, Payame Noor University,
Shahnaz Alley Haj Mahmood Norian Street,
$$AND$$
Tabriz College of
Technology, P. O. Box 51745-135, Tabriz, Iran.
PhD and Graduate Center, Payame Noor University,
Shahnaz Alley Haj Mahmood Norian Street,
$$AND$$
Tabriz College of
Technology, P. O. Box 51745-135, Tabriz, Iran.
LEAD_AUTHOR
ORIGINAL_ARTICLE
Fuzzy approximately additive mappings
Moslehian and Mirmostafaee, investigated the fuzzystability problems for the Cauchy additive functional equation, the Jensen additivefunctional equation and the cubic functional equation in fuzzyBanach spaces. In this paper, we investigate thegeneralized Hyers–-Ulam--Rassias stability of the generalizedadditive functional equation with $n$--variables, in fuzzy Banachspaces. Also, we will show that there exists a close relationshipbetween the fuzzy continuity behavior of a fuzzy almost additivefunction, control function and the unique additive function whichapproximate the almost additive function.
https://ijnaa.semnan.ac.ir/article_74_03299cf23773f3e7dad90060197c6926.pdf
2010-06-01T11:23:20
2020-01-25T11:23:20
44
53
10.22075/ijnaa.2010.74
Fuzzy stability
Additive functional
equation
Fuzzy normed space
H.
Khodaei
true
1
Department of Mathematics,
Semnan University P. O. Box 35195-363, Semnan, Iran.
Department of Mathematics,
Semnan University P. O. Box 35195-363, Semnan, Iran.
Department of Mathematics,
Semnan University P. O. Box 35195-363, Semnan, Iran.
LEAD_AUTHOR
M.
Kamyar
true
2
Department of Mathematics,
Semnan University P. O. Box 35195-363, Semnan, Iran.
Department of Mathematics,
Semnan University P. O. Box 35195-363, Semnan, Iran.
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, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional 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 homomorphismsin Banach algebras and of derivations on Banach algebras associatedwith the generalized additive functional inequality (0.1).
https://ijnaa.semnan.ac.ir/article_75_d483822afcaa756db55cc195d4bd784d.pdf
2010-06-01T11:23:20
2020-01-25T11:23:20
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
true
1
Department of Mathematics, Hanyang University,
Seoul 133-791, Republic of Korea.
Department of Mathematics, Hanyang University,
Seoul 133-791, Republic of Korea.
Department of Mathematics, Hanyang University,
Seoul 133-791, Republic of Korea.
LEAD_AUTHOR
A.
Najati
true
2
Faculty of Sciences, Department of Mathematics,
University of Mohaghegh Ardabili,
Ardabil,
Islamic Republic of Iran.
Faculty of Sciences, Department of Mathematics,
University of Mohaghegh Ardabili,
Ardabil,
Islamic Republic of Iran.
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 withthe 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 $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda 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 $a,bin mathcal A.$ In this paper, our main purpose is to prove thegeneralized Hyers –- Ulam –- Rassias stability of Lie $*$ -double derivations on Lie $C^*$ - algebras associated with thefollowing additive mapping:begin{align*}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, ineqi_{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}) end{align*} for a fixed positive integer $n$ with $n geq 2.$
https://ijnaa.semnan.ac.ir/article_76_53a185511f0f7605fd4bc2aa5437e49a.pdf
2010-06-01T11:23:20
2020-01-25T11:23:20
63
71
10.22075/ijnaa.2010.76
Generalized Hyers -- Ulam -- Rassias
stability
$*$ -- double derivation
Lie $C^*$ -- algebra
N.
Ghobadipour
true
1
Department of Mathematics,
Urmia University, Urmia, Iran.
Department of Mathematics,
Urmia University, Urmia, Iran.
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 functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $mathcal{L}$-fuzzy normed spaces.
https://ijnaa.semnan.ac.ir/article_77_f653e0485a7b895e88a5a8030a62f80c.pdf
2010-06-01T11:23:20
2020-01-25T11:23:20
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
true
1
Department of Mathematics,
Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran.}
Department of Mathematics,
Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran.}
Department of Mathematics,
Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran.}
AUTHOR
R.
Saadati
true
2
Department of Mathematics,
Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran.}
Department of Mathematics,
Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran.}
Department of Mathematics,
Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran.}
AUTHOR
C.
Park
true
3
Department of Mathematics, Research Institute for Natural Sciences,
Hanyang University,
Seoul 133-791, Korea.
Department of Mathematics, Research Institute for Natural Sciences,
Hanyang University,
Seoul 133-791, Korea.
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 generalizedHyers-Ulam-Rassias stability for the quartic, cubic and additivefunctional 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
2010-06-01T11:23:20
2020-01-25T11:23:20
84
99
10.22075/ijnaa.2010.78
stability
QCA--functional equation
$p-$Banach space
S.
Zolfaghari
true
1
Department of Mathematics,
Urmia University, Urmia, Iran.
Department of Mathematics,
Urmia University, Urmia, Iran.
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--Ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy Banach spaces.
https://ijnaa.semnan.ac.ir/article_79_0f500f465e1383e760d9492604334fca.pdf
2010-06-01T11:23:20
2020-01-25T11:23:20
100
124
10.22075/ijnaa.2010.79
Intuitionistic fuzzy normed space
Mixed functional equation
Intuitionistic fuzzy stability
S.
Abbaszadeh
true
1
Department of Mathematics, Semnan
University, P. O. Box 35195-363,
Semnan, Iran.
Department of Mathematics, Semnan
University, P. O. Box 35195-363,
Semnan, Iran.
Department of Mathematics, Semnan
University, P. O. Box 35195-363,
Semnan, Iran.
LEAD_AUTHOR