2020-01-25T23:44:32Z https://ijnaa.semnan.ac.ir/?_action=export&rf=summon&issue=17
2010-06-01 10.22075
International Journal of Nonlinear Analysis and Applications IJNAA 2010 1 2 Isomorphisms in unital \$C^*\$-algebras C. Park Th. M. Rassias 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 2010 06 01 1 10 https://ijnaa.semnan.ac.ir/article_62_c9da465ab255a2d53f17b3a6cdf00d84.pdf
2010-06-01 10.22075
International Journal of Nonlinear Analysis and Applications IJNAA 2010 1 2 A new method for the generalized Hyers-Ulam-Rassias stability P. Gavruta L. Gavruta 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 2010 06 01 11 18 https://ijnaa.semnan.ac.ir/article_70_53c5dcd77c8d0bb23122772e4b5b6a97.pdf
2010-06-01 10.22075
International Journal of Nonlinear Analysis and Applications IJNAA 2010 1 2 Hyers-Ulam stability of Volterra integral equation M. Gachpazan O. Baghani 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 2010 06 01 19 25 https://ijnaa.semnan.ac.ir/article_71_d9b6a3c6b2cef34d8b142ca405cf0387.pdf
2010-06-01 10.22075
International Journal of Nonlinear Analysis and Applications IJNAA 2010 1 2 stability of the quadratic functional equation E. Elqorachi Y. Manar Th. M. Rassias 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 2010 06 01 26 35 https://ijnaa.semnan.ac.ir/article_72_80bd73337686e609bb56f0fac56e6130.pdf
2010-06-01 10.22075
International Journal of Nonlinear Analysis and Applications IJNAA 2010 1 2 Approximately higher Hilbert \$C^*\$-module derivations M. B. Ghaemi B. Alizadeh 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 2010 06 01 36 43 https://ijnaa.semnan.ac.ir/article_73_fee714a36aebab5998d94504bea16488.pdf
2010-06-01 10.22075
International Journal of Nonlinear Analysis and Applications IJNAA 2010 1 2 Fuzzy approximately additive mappings H. Khodaei M. Kamyar 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 2010 06 01 44 53 https://ijnaa.semnan.ac.ir/article_74_03299cf23773f3e7dad90060197c6926.pdf
2010-06-01 10.22075
International Journal of Nonlinear Analysis and Applications IJNAA 2010 1 2 Generalized additive functional inequalities in Banach algebras C. Park A. Najati 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 2010 06 01 54 62 https://ijnaa.semnan.ac.ir/article_75_d483822afcaa756db55cc195d4bd784d.pdf
2010-06-01 10.22075
International Journal of Nonlinear Analysis and Applications IJNAA 2010 1 2 Lie \$^*\$-double derivations on Lie \$C^*\$-algebras N. Ghobadipour 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 2010 06 01 63 71 https://ijnaa.semnan.ac.ir/article_76_53a185511f0f7605fd4bc2aa5437e49a.pdf
2010-06-01 10.22075
International Journal of Nonlinear Analysis and Applications IJNAA 2010 1 2 Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces S. Shakeri R. Saadati C. Park 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 2010 06 01 72 83 https://ijnaa.semnan.ac.ir/article_77_f653e0485a7b895e88a5a8030a62f80c.pdf
2010-06-01 10.22075
International Journal of Nonlinear Analysis and Applications IJNAA 2010 1 2 Stability of generalized QCA-functional equation in P-Banach spaces S. Zolfaghari 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 2010 06 01 84 99 https://ijnaa.semnan.ac.ir/article_78_f302ba7732cdf643ccca509d52760006.pdf
2010-06-01 10.22075
International Journal of Nonlinear Analysis and Applications IJNAA 2010 1 2 Intuitionistic fuzzy stability of a quadratic and quartic functional equation S. Abbaszadeh 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 2010 06 01 100 124 https://ijnaa.semnan.ac.ir/article_79_0f500f465e1383e760d9492604334fca.pdf