2010
1
2
2
0
1

Isomorphisms in unital $C^*$algebras
https://ijnaa.semnan.ac.ir/article_62.html
10.22075/ijnaa.2010.62
1
It is shown that every almost linear bijection $h : Arightarrow B$ 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 $nin mathbb Z$, 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 $nin mathbb Z$. 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.
0

1
10


C.
Park
Department of Mathematics, Hanyang University,
Seoul 133791, Republic of Korea
Korea


Th. M.
Rassias
Department of Mathematics,
National Technical
University of Athens,
Zografou Campus, 15780 Athens, Greece
Greece
generalized HyersUlam stability
$C^*$algebra isomorphism
real rank zero
isometry
1

A new method for the generalized HyersUlamRassias stability
https://ijnaa.semnan.ac.ir/article_70.html
10.22075/ijnaa.2010.70
1
We propose a new method, called the weighted space method, for the study of the generalized HyersUlamRassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.
0

11
18


P.
Gavruta
Department of Mathematics,
University "Politehnica" of Timisoara, 300006, Timisoara, Romania
Romania


L.
Gavruta
Department of Mathematics,
University "Politehnica" of Timisoara, 300006, Timisoara, Romania
Romania
Hyers–UlamRassias stability
functional equation
Volterra integral operator
Fredholm integral operator
Weighted space method
1

HyersUlam stability of Volterra integral equation
https://ijnaa.semnan.ac.ir/article_71.html
10.22075/ijnaa.2010.71
1
We will apply the successive approximation method for proving the HyersUlam stability of a linear integral equation of the second kind.
0

19
25


M.
Gachpazan
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran.
Iran


O.
Baghani
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran.
Iran
HyersUlam stability
Banach's fixed point theorem
Volterra integral equation
Successive approximation method
1

stability of the quadratic functional equation
https://ijnaa.semnan.ac.ir/article_72.html
10.22075/ijnaa.2010.72
1
In the present paper a solution of the generalized quadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$
is given where $sigma$ is an involution of the normed space $E$ and $k$ is a fixed positive integer. Furthermore we investigate the HyersUlamRassias stability of the functional equation. The HyersUlam stability on unbounded domains is also studied. Applications of the results for the asymptotic behavior of the generalized quadratic functional equation are provided.
0

26
35


E.
Elqorachi
Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco
Morocco


Y.
Manar
Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco
Morocco


Th. M.
Rassias
Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece
Greece
HyersUlamRassias stability
quadratic functional equation
1

Approximately higher Hilbert $C^*$module derivations
https://ijnaa.semnan.ac.ir/article_73.html
10.22075/ijnaa.2010.73
1
We show that higher derivations on a Hilbert $C^{*}$module associated with the Cauchy functional equation satisfying generalized HyersUlam stability.
0

36
43


M. B.
Ghaemi
Department of Mathematics, Iran
University of Science and Technology, Tehran, Iran
Iran


B.
Alizadeh
PhD and Graduate Center, Payame Noor University,
Shahnaz Alley Haj Mahmood Norian Street, Shiraz, Iran
Iran
HyersUlam stability
Hilbert $C^{*}$modules
Derivation
Higher derivation
Fixed point theorem
1

Fuzzy approximately additive mappings
https://ijnaa.semnan.ac.ir/article_74.html
10.22075/ijnaa.2010.74
1
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–UlamRassias 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.
0

44
53


H.
Khodaei
Department of Mathematics,
Semnan University P. O. Box 35195363, Semnan, Iran.
Iran


M.
Kamyar
Department of Mathematics,
Semnan University P. O. Box 35195363, Semnan, Iran.
Iran
Fuzzy stability
Additive functional equation
Fuzzy normed space
1

Generalized additive functional inequalities in Banach algebras
https://ijnaa.semnan.ac.ir/article_75.html
10.22075/ijnaa.2010.75
1
Using the HyersUlamRassias stability method, we investigate isomorphisms in Banach algebras and derivations on Banach algebras associated with the following generalized additive functional inequalitybegin{eqnarray}af(x)+bf(y)+cf(z) le f(alpha x+ beta y+gamma z) .end{eqnarray}Moreover, we prove the HyersUlamRassias stability of homomorphism in Banach algebras and of derivations on Banach algebras associated with the generalized additive functional inequality (0.1).
0

54
62


C.
Park
Department of Mathematics, Hanyang University,
Seoul 133791, Republic of Korea
Korea


A.
Najati
Faculty of Sciences, Department of Mathematics,
University of Mohaghegh Ardabili,
Ardabil,
Islamic Republic of Iran.
Iran
HyersUlamRassias stability
generalized additive functional inequality
algebra homomorphism in Banach algebra
derivation on Banach algebra
1

Lie $^*$double derivations on Lie $C^*$algebras
https://ijnaa.semnan.ac.ir/article_76.html
10.22075/ijnaa.2010.76
1
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 $a,bin mathcal{A}$. 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:$$sum^{n}_{k=2}(sum^{k}_{i_{1}=2} sum^{k+1}_{i_{2}=i_{1}+1}...sum^{n}_{i_{nk+1}=i_{nk}+1}) f(sum^{n}_{i=1, ineqi_{1},..,i_{nk+1} } x_{i}sum^{nk+1}_{ r=1}x_{i_{r}})+f(sum^{n}_{ i=1} x_{i})=2^{n1} f(x_{1})$$ for a fixed positive integer $n$ with $n geq 2.$
0

63
71


N.
Ghobadipour
Department of Mathematics,
Urmia University, Urmia, Iran.
Iran
Generalized HyersUlamRassias stability
$*$double derivation
Lie $C^*$algebra
1

Stability of the quadratic functional equation in nonArchimedean Lfuzzy normed spaces
https://ijnaa.semnan.ac.ir/article_77.html
10.22075/ijnaa.2010.77
1
In this paper, we prove the generalized HyersUlam stability of the quadratic functional equation$$f(x+y)+f(xy)=2f(x)+2f(y)$$in nonArchimedean $mathcal{L}$fuzzy normed spaces.
0

72
83


S.
Shakeri
Department of Mathematics,
Islamic Azad UniversityAiatollah Amoli Branch, Amol, P.O. Box 678, Iran
Iran


R.
Saadati
Department of Mathematics,
Islamic Azad UniversityAiatollah Amoli Branch, Amol, P.O. Box 678, Iran
Iran


C.
Park
Department of Mathematics, Research Institute for Natural Sciences, Hanyang University,
Seoul 133791, Korea
Korea
$mathcal{L}$fuzzy metric and normed spaces
intuitionistic fuzzy metric and normed spaces
generalized HyersUlam stability
quadratic functional equation
nonArchimedean $mathcal{L}$fuzzy normed space
1

Stability of generalized QCAfunctional equation in PBanach spaces
https://ijnaa.semnan.ac.ir/article_78.html
10.22075/ijnaa.2010.78
1
In this paper, we investigate the generalized HyersUlamRassias stability for the quartic, cubic and additive functional equation$$f(x+ky)+f(xky)=k^2f(x+y)+k^2f(xy)+(k^21)[k^2f(y)+k^2f(y)2f(x)]$$ ($k in mathbb{Z}{0,pm1}$) in $p$Banach spaces.
0

84
99


S.
Zolfaghari
Department of Mathematics,
Urmia University, Urmia, Iran.
Iran
stability
QCAfunctional equation
$p$Banach space
1

Intuitionistic fuzzy stability of a quadratic and quartic functional equation
https://ijnaa.semnan.ac.ir/article_79.html
10.22075/ijnaa.2010.79
1
In this paper, we prove the generalized HyersUlam stability of a quadratic and quartic functional equation in intuitionistic fuzzy Banach spaces.
0

100
124


S.
Abbaszadeh
Department of Mathematics, Semnan
University, P. O. Box 35195363,
Semnan, Iran.
Iran
Intuitionistic fuzzy normed space
Mixed functional equation
Intuitionistic fuzzy stability