A evolução do projeto F-X em F-X2: a disputa de empresas transnacionais em procedimento licitatório para a venda de caças supersônicos com irrestrita transferência de tecnologia para o Brasil by Roberto Vinícius Hartmann, Luís Alexandre Carta Winter

“…Palavras-chave: Políticas públicas. Projeto F-X. Projeto F-X2. Transferência de tecnologia. Empresa transnacional. …”
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Inner product spaces and quadratic functional equations by Jae-Hyeong Bae, Batool Noori, M. B. Moghimi, Abbas Najati

“…Abstract In this paper, we introduce the functional equations f ( 2 x − y ) + f ( x + 2 y ) = 5 [ f ( x ) + f ( y ) ] , f ( 2 x − y ) + f ( x + 2 y ) = 5 f ( x ) + 4 f ( y ) + f ( − y ) , f ( 2 x − y ) + f ( x + 2 y ) = 5 f ( x ) + f ( 2 y ) + f ( − y ) , f ( 2 x − y ) + f ( x + 2 y ) = 4 [ f ( x ) + f ( y ) ] + [ f ( − x ) + f ( − y ) ] . …”
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Quantum differentiability of essentially bounded functions on Euclidean space by Lord, S, McDonald, E, Sukochev, F, Zanin, D

“…We prove the condition that the function x↦‖(∇f)(x)‖ 2 d :=((∂ 1 f)(x) 2 +…+(∂ d f)(x) 2 ) d/2 , x∈R d , being integrable is necessary and sufficient for the quantised derivative of f to belong to the weak Schatten d-class. …”

The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces by Thanyacharoen Anurak, Sintunavarat Wutiphol

“…In this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x−3y)+f(x+2y)+f(x−2y)+22f(x)+24f(y)=13[f(x+y)+f(x−y)]+12f(2y),f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.…”
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A rough differentiable function by Kirchheim, B, Mueller, P

“…A real-valued continuously differentiable function f on the unit interval is constructed such that Γk=1∞ βf(x,2-k)=∞ holds for every x ∈ [0, 1]. Here βf(x, 2-k) measures the distance of f to the best approximating linear function at scale 2-k around x. © 2008 by the authors.…”

On the Stability of a Cubic Functional Equation in Random Normed Spaces by H. Azadi Kenary

“…Recently, the Hyers-Ulam-Rassias stability of the functional equation f(x + 2y) + f(x − 2y) = 2f(x) − f(2x) + 4n f(x + y) + f(x − y) o , has been proved in the case of Banach spaces. …”
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Fuzzy Stability of Quadratic Functional Equations by Dong Yun Shin, Choonkil Park, Sun-Young Jang, Jung Rye Lee

“…In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations f(x+y)+f(x−y)=2f(x)+2f(y) and f(ax+by)+f(ax−by)=2a2f(x)+2b2f(y)  (a,b∈ℝ\{0},a≠±1) in fuzzy Banach spaces.…”
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On certain functional equation in prime rings by Fošner Maja, Marcen Benjamin, Vukman Joso

“…Let RR be prime ring of characteristic different from two and three, and let F:R→RF:R\to R be an additive mapping satisfying the relation F(x3)=F(x2)x−xF(x)x+xF(x2)F\left({x}^{3})=F\left({x}^{2})x-xF\left(x)x+xF\left({x}^{2}) for all x∈Rx\in R. …”
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Global maximal inequality to a class of oscillatory integrals by Ying Xue, Yaoming Niu

“…Abstract In the present paper, we give the global Lq $L^{q}$ estimates for maximal operators generated by multiparameter oscillatory integral St,Φ $S_{t,\varPhi}$, which is defined by St,Φf(x)=(2π)−n∫Rneix⋅ξei(t1ϕ1(|ξ1|)+t2ϕ2(|ξ2|)+⋯+tnϕn(|ξn|))fˆ(ξ)dξ,x∈Rn, $$S_{t,\varPhi}f(x)=(2\pi)^{-n} \int_{\mathbb{R}^{n}} e^{ix\cdot\xi}e^{i(t_{1} \phi_{1}(|\xi_{1}|)+t_{2}\phi_{2}(|\xi_{2}|)+ \cdots+t_{n}\phi_{n}(|\xi_{n}|))}\hat{f}(\xi)\,d\xi,\quad x\in\mathbb{R}^{n}, $$ where n≥2 $n\geq2$ and f is a Schwartz function in S(Rn) $\mathcal{S}(\mathbb {R}^{n})$, t=(t1,t2,…,tn) $t=(t_{1},t_{2},\ldots,t_{n})$, Φ=(ϕ1,ϕ2,…,ϕn) $\varPhi=(\phi_{1},\phi_{2},\ldots,\phi_{n})$, ϕi $\phi_{i}$ (i=1,2,3,…,n) $(i=1,2,3,\ldots, n)$ is a function on R+→R $\mathbb {R}^{+}\rightarrow\mathbb{R}$, which has a suitable growth condition. …”
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Stability of an Additive-Cubic-Quartic Functional Equation by M. Eshaghi-Gordji, S. Kaboli-Gharetapeh, Choonkil Park, Somayyeh Zolfaghari

“…In this paper, we consider the additive-cubic-quartic functional equation 11[f(x+2y)+f(x−2y)]=44[f(x+y)+f(x−y)]+12f(3y)−48f(2y)+60f(y)−66f(x) and prove the generalized Hyers-Ulam stability of the additive-cubic-quartic functional equation in Banach spaces.…”
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Stability of Mixed Type Cubic and Quartic Functional Equations in Random Normed Spaces by M. Eshaghi Gordji, M. B. Savadkouhi

“…We obtain the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary t-norms f(x+2y)+f(x−2y)=4[f(x+y)+f(x−y)]−24f(y)−6f(x)+3f(2y).…”
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On Some Uniform Bounds for Smooth Algebraic Functions by A. PARMEGGIANI

“…As a byproduct, it is shown that x !−→ (y −f(x))2, where f is a smooth algebraic function, behaves like a polynomial (in terms of scaling properties of averages and maxima). …”
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Stability Problems of Quintic Mappings in Quasi-β-Normed Spaces by In Goo Cho, Dongseung Kang, Heejeong Koh

“…We investigate the generalized Hyers-Ulam-Rassias stability problem in quasi-β-normed spaces and then the stability by using a subadditive function for the quintic function f:X→Y such that 2f(2x+y)+2f(2x−y)+f(x+2y)+f(x−2y)=20[f(x+y)+f(x−y)]+90f(x), for all x,y∈X.…”
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Remarks on solutions to the functional equations of the radical type by Janusz Brzdęk

“…Simple natural examples of them are the following two functional equations fn √xn + yn= f(x) + f(y),f n √xn + yn+ fn p|xn −yn|= 2f(x) + 2f(y) considered recently in several papers, for real functions and with given positive integer n, in connection with the notion of Ulam (or Hyers-Ulam) stability. …”
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Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras by Choonkil Park

“…We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: f(x+y/2+z)+f(x−y/2+z)=f(x)+2f(z), 2f(x+y/2+z)=f(x)+f(y)+2f(z), which were introduced and investigated by Baak (2006). …”
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New results on topological dynamics of antitriangular maps by Francisco Balibrea, J.S. Cánovas, A. Linero

“…We present some results concerning the topological dynamics of antitriangular maps, F:X2→ X2 with the formvF(x,y)=(g(y),f(x)), where (X,d) is a compact metric space and f,g : X→ X are continuous maps. …”
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An observation on spaces with a zeroset diagonal by Wei-Feng Xuan

“…A space $X$ has a zeroset diagonal if there is a continuous mapping $f X^2 \rightarrow[0,1]$ with $\Delta_X=f^{-1}(0)$, where $\Delta_X=\{(x,x)\colon x\in X\}$. …”
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Diagonals of separately continuous maps with values in box products by Karlova Olena, Mykhaylyuk Volodymyr

“…We prove that if X is a paracompact connected space and Z = ∏s∈S Zs is a product of a family of equiconnected metrizable spaces endowed with the box topology, then for every Baire-one map g : X → Z there exists a separately continuous map f : X2 → Z such that f (x, x) = g(x) for all x ∈ X.…”
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Fuzzy Stability of an Additive-Quadratic-Quartic Functional Equation by Choonkil Park

“…Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation: f(x+2y)+f(x−2y)=2f(x+y)+2f(−x−y)+2f(x−y)+2f(y−x)−4f(−x)−2f(x)+f(2y)+f(−2y)−4f(y)−4f(−y) in fuzzy Banach spaces.…”
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On stability of the functional equation of p-Wright affine functions in (2, α)-Banach spaces by El-sayed El-hady

“…Brzdęk and concerning the functional equation of the p-Wright affine function: f(p x 1+(1−p)x 2)+f((1−p)x 1+p x 2)=f(x 1)+f(x 2), can be proved also in (2, α)-Banach spaces, for some real number α∈(0,1). …”
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