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Mechanical Characterization of Intermaxillary Orthodontic Elastics: Energy-Based Metrics and Clinical Guidance. [PDF]

J Funct Biomater
Antunes P, Oliveira C, Santos M, Marto CM, Vilhena L, Ramalho A, Francisco I, Vale F.   +7 more
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A Generalized Cubic Functional Equation

Acta Mathematica Sinica, English Series, 2005
The author solves the functional equation \[ f_1(2x+y)+f_2(2x-y)=f_3(x+y)+f_4(x-y)+f_5(x), \qquad x,y \in \mathbb R, \] where \(f_1, f_2, f_3, f_4, f_5: \mathbb R \to \mathbb R\). The general solution, obtained by elementary methods, is made up via diagonal of multiadditive symmetric functions. This result is then extended to the case of functions from
Sahoo P K
exaly   +2 more sources

Hyperstability of cubic functional equation in banach space

Annali Dell'Universita Di Ferrara, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohamed Rossafi, Rossafi Mohamed
exaly   +2 more sources

On the stability of a cubic functional equation

Acta Mathematica Sinica, English Series, 2008
The authors consider the functional equation \[ 2f(x+2y)+f(2x-y)=5f(x+y)+5f(x-y)+15f(y). \] They determine the general solution and the generalized Hyers-Ulam-Rassias stability of the functional equation.
Choonkil Park, Abbas Najati, Park Choonkil   +2 more
exaly   +3 more sources

Solution and stability of a cubic functional equation

Acta Mathematica Sinica, English Series, 2010
Similar to the method used by \textit{H.-Y Chu} and \textit{D.-S. Kang} [J. Math. Anal. Appl. 325, No.~1, 595--607 (2007; Zbl 1106.39025)] and \textit{A. Najati} and \textit{Ch. Park} [Acta Math. Sin., Engl. Ser. 24, No.~12, 1953--1964 (2008; Zbl 1159.39014)], the authors obtain the general solution and investigate the stability of the following cubic ...
Jun, Kil Woung, Lee, Sang Baek, Park, Won Gil   +2 more
exaly   +3 more sources

The generalized cubic functional equation and the stability of cubic Jordan $$*$$ ∗ -derivations

Annali Dell'Universita Di Ferrara, 2013
Several definitions of ``cubic functional equations'' have been already given. Here, the authors introduce a new one: \[ \begin{multlined} f(x+my)+f(x-my) =2(2\cos\left(\frac{m\pi}{2}\right)+m^2-1)f(x)\\ -\frac{1}{2}(\cos\left(\frac{m\pi}{2}\right)+m^2-1)f(2x) +m^4(f(x+y)+f(x-y)), \end{multlined} \] where \(m\) is an integer not less than 2.
Abasalt Bodaghi, Hamidreza Rahimi, Bodaghi Abasalt   +2 more
exaly   +2 more sources

Fuzzy stability for a class of cubic functional equations

Journal of Intelligent & Fuzzy Systems, 2017
In this paper, we investigate the following typical form of a class of cubic functional equations:
Chang-Il Kim 0002, Giljun Han
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Fuzzy approximations of a multiplicative inverse cubic functional equation

Soft Computing, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
B. V. Senthil Kumar, Hemen Dutta, S. Sabarinathan   +2 more
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DIFFERENTIAL EQUATIONS FOR CUBIC THETA FUNCTIONS

International Journal of Number Theory, 2011
We show that the cubic theta functions satisfy two distinct coupled systems of nonlinear differential equations. The resulting relations are analogous to Ramanujan's differential equations for Eisenstein series on the full modular group. We deduce the cubic analogs presented here from trigonometric series identities arising in Ramanujan's original ...
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Fuzzy stability of quadratic-cubic functional equations

Acta Mathematica Sinica, English Series, 2011
The authors consider the functional equation, derived from cubic and quadratic functions: \[ 6f(x+y)-6f(x-y)+4f(3y)=3f(x+2y)-3f(x-2y)+9f(2y), \] and apply the direct method and the fixed point alternative method to obtain the Hyers-Ulam-Rassias stability for that equation in fuzzy Banach spaces.
Wang, Zhi Hua, Zhang, Wan Xiong
openaire   +2 more sources