@article {
author = {Park, C. and Rassias, Th. M.},
title = {Isomorphisms in unital $C^*$-algebras},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {1},
number = {2},
pages = {1-10},
year = {2010},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2010.62},
abstract = {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.},
keywords = {generalized Hyers-Ulam stability,$C^*$-algebra isomorphism,real rank zero,isometry},
url = {https://ijnaa.semnan.ac.ir/article_62.html},
eprint = {https://ijnaa.semnan.ac.ir/article_62_c9da465ab255a2d53f17b3a6cdf00d84.pdf}
}
@article {
author = {Gavruta, P. and Gavruta, L.},
title = {A new method for the generalized Hyers-Ulam-Rassias stability},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {1},
number = {2},
pages = {11-18},
year = {2010},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2010.70},
abstract = {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.},
keywords = {Hyers–-Ulam--Rassias stability,functional equation,Volterra integral operator,Fredholm integral
operator,Weighted space method},
url = {https://ijnaa.semnan.ac.ir/article_70.html},
eprint = {https://ijnaa.semnan.ac.ir/article_70_53c5dcd77c8d0bb23122772e4b5b6a97.pdf}
}
@article {
author = {Gachpazan, M. and Baghani, O.},
title = {Hyers-Ulam stability of Volterra integral equation},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {1},
number = {2},
pages = {19-25},
year = {2010},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2010.71},
abstract = {We will apply the successive approximation method for proving the Hyers--Ulam stability of a linear integral equation of the second kind.},
keywords = {Hyers--Ulam stability,Banach's fixed point theorem,Volterra integral equation,Successive approximation method},
url = {https://ijnaa.semnan.ac.ir/article_71.html},
eprint = {https://ijnaa.semnan.ac.ir/article_71_d9b6a3c6b2cef34d8b142ca405cf0387.pdf}
}
@article {
author = {Elqorachi, E. and Manar, Y. and Rassias, Th. M.},
title = {stability of the quadratic functional
equation},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {1},
number = {2},
pages = {26-35},
year = {2010},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2010.72},
abstract = {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.},
keywords = {Hyers-Ulam-Rassias stability,quadratic functional equation},
url = {https://ijnaa.semnan.ac.ir/article_72.html},
eprint = {https://ijnaa.semnan.ac.ir/article_72_80bd73337686e609bb56f0fac56e6130.pdf}
}
@article {
author = {Ghaemi, M. B. and Alizadeh, B.},
title = {Approximately higher Hilbert $C^*$-module derivations},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {1},
number = {2},
pages = {36-43},
year = {2010},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2010.73},
abstract = {We show that higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability. },
keywords = {Hyers--Ulam stability,Hilbert
$C^{*}-$modules,Derivation,Higher derivation,fixed point
theorem},
url = {https://ijnaa.semnan.ac.ir/article_73.html},
eprint = {https://ijnaa.semnan.ac.ir/article_73_fee714a36aebab5998d94504bea16488.pdf}
}
@article {
author = {Khodaei, H. and Kamyar, M.},
title = {Fuzzy approximately additive mappings},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {1},
number = {2},
pages = {44-53},
year = {2010},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2010.74},
abstract = {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.},
keywords = {Fuzzy stability,Additive functional
equation,Fuzzy normed space},
url = {https://ijnaa.semnan.ac.ir/article_74.html},
eprint = {https://ijnaa.semnan.ac.ir/article_74_03299cf23773f3e7dad90060197c6926.pdf}
}
@article {
author = {Park, C. and Najati, A.},
title = {Generalized additive functional
inequalities in Banach algebras},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {1},
number = {2},
pages = {54-62},
year = {2010},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2010.75},
abstract = {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).},
keywords = {Hyers-Ulam-Rassias stability,generalized additive functional inequality,algebra homomorphism in
Banach algebra,derivation on Banach algebra},
url = {https://ijnaa.semnan.ac.ir/article_75.html},
eprint = {https://ijnaa.semnan.ac.ir/article_75_d483822afcaa756db55cc195d4bd784d.pdf}
}
@article {
author = {Ghobadipour, N.},
title = {Lie $^*$-double derivations on Lie $C^*$-algebras},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {1},
number = {2},
pages = {63-71},
year = {2010},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2010.76},
abstract = {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 $n geq 2.$},
keywords = {Generalized Hyers -- Ulam -- Rassias
stability,$*$ -- double derivation,Lie $C^*$ -- algebra},
url = {https://ijnaa.semnan.ac.ir/article_76.html},
eprint = {https://ijnaa.semnan.ac.ir/article_76_53a185511f0f7605fd4bc2aa5437e49a.pdf}
}
@article {
author = {Shakeri, S. and Saadati, R. and Park, C.},
title = {Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {1},
number = {2},
pages = {72-83},
year = {2010},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2010.77},
abstract = {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.},
keywords = {$mathcal{L}$-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},
url = {https://ijnaa.semnan.ac.ir/article_77.html},
eprint = {https://ijnaa.semnan.ac.ir/article_77_f653e0485a7b895e88a5a8030a62f80c.pdf}
}
@article {
author = {Zolfaghari, S.},
title = {Stability of generalized QCA-functional equation in P-Banach spaces},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {1},
number = {2},
pages = {84-99},
year = {2010},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2010.78},
abstract = {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.},
keywords = {stability,QCA--functional equation,$p-$Banach space},
url = {https://ijnaa.semnan.ac.ir/article_78.html},
eprint = {https://ijnaa.semnan.ac.ir/article_78_f302ba7732cdf643ccca509d52760006.pdf}
}
@article {
author = {Abbaszadeh, S.},
title = {Intuitionistic fuzzy stability of a
quadratic and quartic functional equation},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {1},
number = {2},
pages = {100-124},
year = {2010},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2010.79},
abstract = {In this paper, we prove the generalized Hyers--Ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy Banach spaces.},
keywords = {Intuitionistic fuzzy normed space,Mixed functional equation,Intuitionistic fuzzy stability},
url = {https://ijnaa.semnan.ac.ir/article_79.html},
eprint = {https://ijnaa.semnan.ac.ir/article_79_0f500f465e1383e760d9492604334fca.pdf}
}