Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 06 01 Isomorphisms in unital \$C^*\$-algebras 1 10 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 10.22075/ijnaa.2010.62 It is shown that every  almost linear bijection \$h : A<br />rightarrow B\$ of a unital \$C^*\$-algebra \$A\$ onto a unital<br />\$C^*\$-algebra \$B\$ is a \$C^*\$-algebra isomorphism when<br /> \$h(3^n u y) = h(3^n u) h(y)\$ for all<br />unitaries  \$u in A\$, all \$y in A\$, and all \$nin mathbb Z\$, and<br />that almost linear continuous bijection \$h : A rightarrow B\$ of a<br />unital \$C^*\$-algebra \$A\$ of real rank zero onto a unital<br />\$C^*\$-algebra \$B\$ is a \$C^*\$-algebra isomorphism when  \$h(3^n u y) =<br />h(3^n u) h(y)\$  for all<br />  \$u in { v in A mid v = v^*, |v|=1, v text{ is invertible} }\$, all<br />\$y in A\$, and all \$nin mathbb Z\$.<br /><br />Assume that \$X\$ and \$Y\$  are left normed modules over a unital<br />\$C^*\$-algebra \$A\$. It is shown that every surjective isometry \$T : X<br />rightarrow Y\$, satisfying \$T(0) =0\$ and \$T(ux) = u T(x)\$ for all \$x<br />in X\$ and all unitaries \$u in A\$, is an \$A\$-linear isomorphism.<br />This is applied to investigate \$C^*\$-algebra isomorphisms in unital<br />\$C^*\$-algebras. generalized Hyers-Ulam stability,\$C^*\$-algebra isomorphism,real rank zero,isometry https://ijnaa.semnan.ac.ir/article_62.html https://ijnaa.semnan.ac.ir/article_62_c9da465ab255a2d53f17b3a6cdf00d84.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 06 01 A new method for the generalized Hyers-Ulam-Rassias stability 11 18 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. 10.22075/ijnaa.2010.70 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. Hyers–-Ulam--Rassias stability,functional equation,Volterra integral operator,Fredholm integral operator,Weighted space method https://ijnaa.semnan.ac.ir/article_70.html https://ijnaa.semnan.ac.ir/article_70_53c5dcd77c8d0bb23122772e4b5b6a97.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 06 01 Hyers-Ulam stability of Volterra integral equation 19 25 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. 10.22075/ijnaa.2010.71 We will apply the successive approximation method for<br />proving the Hyers--Ulam stability of a linear integral equation of<br />the second kind. Hyers--Ulam stability,Banach's fixed point theorem,Volterra integral equation,Successive approximation method https://ijnaa.semnan.ac.ir/article_71.html https://ijnaa.semnan.ac.ir/article_71_d9b6a3c6b2cef34d8b142ca405cf0387.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 06 01 stability of the quadratic functional equation 26 35 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 10.22075/ijnaa.2010.72 In the present paper a solution of the generalized<br />quadratic functional equation<br />\$\$<br />f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}\$\$ is<br />given where \$sigma\$ is an involution of the normed space \$E\$ and<br />\$k\$ is a fixed positive integer. Furthermore we investigate the<br />Hyers-Ulam-Rassias stability of the functional equation. The<br />Hyers-Ulam stability on unbounded domains is also studied.<br />Applications of the results for the asymptotic behavior of the<br />generalized quadratic functional equation are provided. Hyers-Ulam-Rassias stability,quadratic functional equation https://ijnaa.semnan.ac.ir/article_72.html https://ijnaa.semnan.ac.ir/article_72_80bd73337686e609bb56f0fac56e6130.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 06 01 Approximately higher Hilbert \$C^*\$-module derivations 36 43 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, \$\$AND\$\$ Tabriz College of Technology, P. O. Box 51745-135, Tabriz, Iran. 10.22075/ijnaa.2010.73 We show that  higher derivations on a Hilbert<br />\$C^{*}-\$module associated with<br /> the Cauchy functional equation satisfying generalized Hyers--Ulam stability. <br />  Hyers--Ulam stability,Hilbert \$C^{*}-\$modules,Derivation,Higher derivation,fixed point theorem https://ijnaa.semnan.ac.ir/article_73.html https://ijnaa.semnan.ac.ir/article_73_fee714a36aebab5998d94504bea16488.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 06 01 Fuzzy approximately additive mappings 44 53 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. 10.22075/ijnaa.2010.74 Moslehian  and Mirmostafaee, investigated the fuzzy<br />stability problems<br /> for the Cauchy additive functional equation, the Jensen additive<br />functional equation and the cubic functional equation in fuzzy<br />Banach spaces.<br /> In this paper, we investigate the<br />generalized Hyers–-Ulam--Rassias stability of the generalized<br />additive functional equation with \$n\$--variables, in fuzzy Banach<br />spaces. Also, we will show that there exists a close relationship<br />between the fuzzy continuity behavior of a fuzzy almost additive<br />function, control function and the unique additive function which<br />approximate the almost additive function. Fuzzy stability,Additive functional equation,Fuzzy normed space https://ijnaa.semnan.ac.ir/article_74.html https://ijnaa.semnan.ac.ir/article_74_03299cf23773f3e7dad90060197c6926.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 06 01 Generalized additive functional inequalities in Banach algebras 54 62 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. 10.22075/ijnaa.2010.75 Using the Hyers-Ulam-Rassias stability method, we<br />investigate isomorphisms in Banach algebras and derivations on<br />Banach algebras associated with the following generalized additive<br />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 homomorphisms<br />in Banach algebras and of derivations on Banach algebras associated<br />with the generalized additive functional inequality (0.1). Hyers-Ulam-Rassias stability,generalized additive functional inequality,algebra homomorphism in Banach algebra,derivation on Banach algebra https://ijnaa.semnan.ac.ir/article_75.html https://ijnaa.semnan.ac.ir/article_75_d483822afcaa756db55cc195d4bd784d.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 06 01 Lie \$^*\$-double derivations on Lie \$C^*\$-algebras 63 71 EN N. Ghobadipour Department of Mathematics, Urmia University, Urmia, Iran. 10.22075/ijnaa.2010.76 A unital \$C^*\$ -- algebra \$mathcal A,\$ endowed with<br />the Lie product \$[x,y]=xy- yx\$ on \$mathcal A,\$ is called a Lie<br />\$C^*\$ -- algebra. Let \$mathcal A\$ be a Lie \$C^*\$ -- algebra and<br />\$g,h:mathcal A to mathcal A\$ be \$Bbb C\$ -- linear mappings. A<br />\$Bbb C\$ -- linear mapping \$f:mathcal A to mathcal A\$ is called<br />a Lie \$(g,h)\$ -- double derivation if<br />\$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]\$ for all \$a,b<br />in mathcal A.\$ In this paper, our main purpose is to prove the<br />generalized Hyers –- Ulam –- Rassias stability  of Lie \$*\$ -<br />double derivations on Lie \$C^*\$ - algebras associated with the<br />following additive mapping:<br />begin{align*}<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 /> end{align*}<br /> for a fixed positive integer \$n\$ with \$n geq 2.\$ Generalized Hyers -- Ulam -- Rassias stability,\$*\$ -- double derivation,Lie \$C^*\$ -- algebra https://ijnaa.semnan.ac.ir/article_76.html https://ijnaa.semnan.ac.ir/article_76_53a185511f0f7605fd4bc2aa5437e49a.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 06 01 Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces 72 83 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. 10.22075/ijnaa.2010.77 In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functional<br />equation<br />\$\$f(x+y)+f(x-y)=2f(x)+2f(y)\$\$<br />in non-Archimedean \$mathcal{L}\$-fuzzy normed spaces. \$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 https://ijnaa.semnan.ac.ir/article_77.html https://ijnaa.semnan.ac.ir/article_77_f653e0485a7b895e88a5a8030a62f80c.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 06 01 Stability of generalized QCA-functional equation in P-Banach spaces 84 99 EN S. Zolfaghari Department of Mathematics, Urmia University, Urmia, Iran. 10.22075/ijnaa.2010.78 In  this paper, we investigate the generalized<br />Hyers-Ulam-Rassias stability for the quartic, cubic and additive<br />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. stability,QCA--functional equation,\$p-\$Banach space https://ijnaa.semnan.ac.ir/article_78.html https://ijnaa.semnan.ac.ir/article_78_f302ba7732cdf643ccca509d52760006.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 1 2 2010 06 01 Intuitionistic fuzzy stability of a quadratic and quartic functional equation 100 124 EN S. Abbaszadeh Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran. 10.22075/ijnaa.2010.79 In this paper, we prove the generalized Hyers--Ulam<br />stability of a quadratic and quartic functional equation in<br />intuitionistic fuzzy Banach spaces. Intuitionistic fuzzy normed space,Mixed functional equation,Intuitionistic fuzzy stability https://ijnaa.semnan.ac.ir/article_79.html https://ijnaa.semnan.ac.ir/article_79_0f500f465e1383e760d9492604334fca.pdf