Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 08 01 Isomorphisms in unital $C^*$-algebras 1 10 62 10.22075/ijnaa.2010.62 EN C. Park Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea Th. M. Rassias Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece Journal Article 2010 01 26 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

Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 08 01 A new method for the generalized Hyers-Ulam-Rassias stability 11 18 70 10.22075/ijnaa.2010.70 EN P. Gavruta Department of Mathematics, University "Politehnica" of Timisoara, 300006, Timisoara, Romania L. Gavruta Department of Mathematics, University "Politehnica" of Timisoara, 300006, Timisoara, Romania Journal Article 2010 04 15 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

Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 07 05 Hyers-Ulam stability of Volterra integral equation 19 25 71 10.22075/ijnaa.2010.71 EN M. Gachpazan Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. O. Baghani Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. Journal Article 2009 04 14 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

Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 08 01 stability of the quadratic functional equation 26 35 72 10.22075/ijnaa.2010.72 EN E. Elqorachi Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco Y. Manar Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco Th. M. Rassias Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece Journal Article 2010 02 12 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

Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 07 05 Approximately higher Hilbert $C^*$-module derivations 36 43 73 10.22075/ijnaa.2010.73 EN M. B. Ghaemi Department of Mathematics, Iran University of Science and Technology, Tehran, Iran B. Alizadeh PhD and Graduate Center, Payame Noor University, Shahnaz Alley Haj Mahmood Norian Street, Shiraz, Iran Tabriz College of Technology, P. O. Box 51745-135, Tabriz, Iran Journal Article 2010 01 10 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

Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 08 01 Fuzzy approximately additive mappings 44 53 74 10.22075/ijnaa.2010.74 EN H. Khodaei Department of Mathematics, Semnan University P. O. Box 35195-363, Semnan, Iran. M. Kamyar Department of Mathematics, Semnan University P. O. Box 35195-363, Semnan, Iran. Journal Article 2010 04 02 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

Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 07 05 Generalized additive functional inequalities in Banach algebras 54 62 75 10.22075/ijnaa.2010.75 EN C. Park Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea A. Najati Faculty of Sciences, Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Islamic Republic of Iran. Journal Article 2010 01 02 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

Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 08 01 Lie $^*$-double derivations on Lie $C^*$-algebras 63 71 76 10.22075/ijnaa.2010.76 EN N. Ghobadipour Department of Mathematics, Urmia University, Urmia, Iran. Journal Article 2010 01 16 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 the following additive mapping: $$ \sum^{n}_{k=2}(\sum^{k}_{i_{1}=2} \sum^{k+1}_{i_{2}=i_{1}+1}... \sum^{n}_{i_{n-k+1}=i_{n-k}+1}) f(\sum^{n}_{i=1, i\neq i_{1},..,i_{n-k+1} } x_{i}-\sum^{n-k+1}_{ r=1}x_{i_{r}})+f(\sum^{n}_{ i=1} x_{i}) =2^{n-1} f(x_{1}) $$ for a fixed positive integer $n$ with $n \geq 2.$

https://ijnaa.semnan.ac.ir/article_76_53a185511f0f7605fd4bc2aa5437e49a.pdf

Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 08 01 Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces 72 83 77 10.22075/ijnaa.2010.77 EN S. Shakeri Department of Mathematics, Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran R. Saadati Department of Mathematics, Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran C. Park Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea Journal Article 2010 04 18 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

Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 07 05 Stability of generalized QCA-functional equation in P-Banach spaces 84 99 78 10.22075/ijnaa.2010.78 EN S. Zolfaghari Department of Mathematics, Urmia University, Urmia, Iran. Journal Article 2010 01 12 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

Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 08 01 Intuitionistic fuzzy stability of a quadratic and quartic functional equation 100 124 79 10.22075/ijnaa.2010.79 EN S. Abbaszadeh Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran. Journal Article 2010 01 18 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