Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601Isomorphisms in unital $C^*$-algebras1106210.22075/ijnaa.2010.62ENC.ParkDepartment of Mathematics, Hanyang University,
Seoul 133-791, Republic of KoreaTh. M.RassiasDepartment of Mathematics,
National Technical
University of Athens,
Zografou Campus, 15780 Athens, GreeceJournal Article20131026It 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601A new method for the generalized Hyers-Ulam-Rassias stability11187010.22075/ijnaa.2010.70ENP.GavrutaDepartment of Mathematics,
University "Politehnica" of Timisoara, 300006, Timisoara, RomaniaL.GavrutaDepartment of Mathematics,
University "Politehnica" of Timisoara, 300006, Timisoara, RomaniaJournal Article20131102We propose a new method, called <em>the weighted space method</em>, 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601Hyers-Ulam stability of Volterra integral equation19257110.22075/ijnaa.2010.71ENM.GachpazanDepartment of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran.O.BaghaniDepartment of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article20131102We will apply the successive approximation method for proving the Hyers--Ulam stability of a linear integral equation of the second kind.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601stability of the quadratic functional equation26357210.22075/ijnaa.2010.72ENE.ElqorachiDepartment of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, MoroccoY.ManarDepartment of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, MoroccoTh. M.RassiasDepartment of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, GreeceJournal Article20131102In the present paper a solution of the generalized quadratic functional equation<br />$$<br />f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$
is given where $sigma$ is an involution of the normed space $E$ and $k$ is a fixed positive integer. Furthermore we investigate the 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601Approximately higher Hilbert $C^*$-module derivations36437310.22075/ijnaa.2010.73ENM. B.GhaemiDepartment of Mathematics, Iran
University of Science and Technology, Tehran, IranB.AlizadehPhD and Graduate Center, Payame Noor University,
Shahnaz Alley Haj Mahmood Norian Street, Shiraz, IranTabriz College of Technology, P. O. Box 51745-135, Tabriz, IranJournal Article20131102We show that higher derivations on a Hilbert $C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability. <br /> Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601Fuzzy approximately additive mappings44537410.22075/ijnaa.2010.74ENH.KhodaeiDepartment of Mathematics,
Semnan University P. O. Box 35195-363, Semnan, Iran.M.KamyarDepartment of Mathematics,
Semnan University P. O. Box 35195-363, Semnan, Iran.Journal Article20131102Moslehian 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601Generalized additive functional inequalities in Banach algebras54627510.22075/ijnaa.2010.75ENC.ParkDepartment of Mathematics, Hanyang University,
Seoul 133-791, Republic of KoreaA.NajatiFaculty of Sciences, Department of Mathematics,
University of Mohaghegh Ardabili,
Ardabil,
Islamic Republic of Iran.Journal Article20131104Using 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<br />begin{eqnarray}<br />|af(x)+bf(y)+cf(z)| le |f(alpha x+ beta y+gamma z)| .<br />end{eqnarray}<br />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).Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601Lie $^*$-double derivations on Lie $C^*$-algebras63717610.22075/ijnaa.2010.76ENN.GhobadipourDepartment of Mathematics,
Urmia University, Urmia, Iran.Journal Article20131104A 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 the<br />following additive mapping:<br />$$<br />sum^{n}_{k=2}(sum^{k}_{i_{1}=2} sum^{k+1}_{i_{2}=i_{1}+1}...<br />sum^{n}_{i_{n-k+1}=i_{n-k}+1}) f(sum^{n}_{i=1, ineq<br />i_{1},..,i_{n-k+1} }<br /> x_{i}-sum^{n-k+1}_{ r=1}x_{i_{r}})+f(sum^{n}_{ i=1} x_{i})<br />=2^{n-1} f(x_{1})<br />$$<br /> for a fixed positive integer $n$ with $n geq 2.$Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces72837710.22075/ijnaa.2010.77ENS.ShakeriDepartment of Mathematics,
Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, IranR.SaadatiDepartment of Mathematics,
Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, IranC.ParkDepartment of Mathematics, Research Institute for Natural Sciences, Hanyang University,
Seoul 133-791, KoreaJournal Article20131104In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functional equation<br />$$f(x+y)+f(x-y)=2f(x)+2f(y)$$<br />in non-Archimedean $mathcal{L}$-fuzzy normed spaces.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601Stability of generalized QCA-functional equation in P-Banach spaces84997810.22075/ijnaa.2010.78ENS.ZolfaghariDepartment of Mathematics,
Urmia University, Urmia, Iran.Journal Article20131104In this paper, we investigate the generalized Hyers-Ulam-Rassias stability for the quartic, cubic and additive functional equation<br />$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$<br /> ($k in mathbb{Z}-{0,pm1}$) in $p-$Banach spaces.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601Intuitionistic fuzzy stability of a quadratic and quartic functional equation1001247910.22075/ijnaa.2010.79ENS.AbbaszadehDepartment of Mathematics, Semnan
University, P. O. Box 35195-363,
Semnan, Iran.Journal Article20131104In this paper, we prove the generalized Hyers--Ulam stability of a quadratic and quartic functional equation in intuitionistic fuzzy Banach spaces.