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 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.
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 \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.
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 forproving the Hyers--Ulam stability of a linear integral equation ofthe 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 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.
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,
$$AND$$
Tabriz College of
Technology, P. O. Box 51745-135, Tabriz, 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 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.
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, 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).
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 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 $n geq 2.$
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 functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$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 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.
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--Ulamstability of a quadratic and quartic functional equation inintuitionistic 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