Results 11 to 20 of about 29,994 (153)
The cubic Pell equation $L$-function
Acta Arithmetica, 2023 For $d > 1$ a cubefree rational integer, we define an $L$-function (denoted $L_d(s)$) whose coefficients are derived from the cubic theta function for $\mathbb Q\left(\sqrt{-3}\right)$. The Dirichlet series defining $L_d(s)$ converges for $\text{Re}(s) > 1$, and its coefficients vanish except at values corresponding to integral solutions of $mx^3
Goldfeld, Dorian, Hinkle, Gerhardt
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ON THE STABILITY OF A GENERALIZED CUBIC FUNCTIONAL EQUATION [PDF]
Bulletin of the Korean Mathematical Society, 2008 Let \(f: X\to Y\) be a mapping between real vector spaces. The functional equation \[ f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)\tag{1} \] is called \textit{cubic equation} and its solution a \textit{cubic function}. The authors investigate a \textit{generalized cubic equation} \[ \begin{multlined} 4f\left(\sum_{j=1}^{n-1}x_j+mx_n\right)+4f\left(\sum_{j=1}^
Koh, Heejeong, Kang, DongSeung
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STABILITY OF A CUBIC FUNCTIONAL EQUATION ON GROUPS [PDF]
Bulletin of the Korean Mathematical Society, 2004 The functional equation \[ f(3x+y)+f(3x-y)=3f(x+y)+3f(x-y)+48f(x)\tag{1} \] is considered for functions mapping an abelian group~\(G\) into a~Banach space~\(X\). Since \(f(x)=cx^3\) fulfils~(1), the authors call it a~{cubic functional equation} and any its solution the {cubic function}. The general solution of~(1) is given. It is of the form \(f(x)=F(x,
Park, Kyoo-Hong, Jung, Yong-Soo
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Approximation of Mixed Euler-Lagrange σ-Cubic-Quartic Functional Equation in Felbin’s Type f-NLS
Journal of Function Spaces, 2021 In this research paper, the authors present a new mixed Euler-Lagrange σ-cubic-quartic functional equation. For this introduced mixed type functional equation, the authors obtain general solution and investigate the various stabilities related to the ...
John Michael Rassias +3 more
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Stabilities of Cubic Mappings in Fuzzy Normed Spaces
Advances in Difference Equations, 2010 Rassias(2001) introduced the pioneering cubic functional equation in the history of mathematical analysis: and solved the pertinent famous Ulam stability problem for this inspiring equation.
Ghaffari Ali, Alinejad Ahmad
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Stability of an l-Variable Cubic Functional Equation
Kragujevac Journal of Mathematics, 2023 Summary: Using the direct and fixed point methods, we obtain the solution and prove the Hyers-Ulam stability of the \(l\)-variable cubic functional equation \begin{align*} & f \left(\sum_{i=1}^l x_i \right) + \sum_{j=1}^l f \left( -lx_j + \sum_{i=1,i \neq j}^l x_i \right) \\ = & -2(l+1) \sum_{i=1,i\neq j \neq k}^l f(x_i + x_j + x_k) + (3l^2 - 2l -5 ...
Govindan, Vediyappan +3 more
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On Approximate Solutions of the Generalized Radical Cubic Functional Equation in Quasi-$beta$-Banach Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2020 In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the generalized radical cubic functional equation[ fleft( sqrt[3]{ax^3 + by^3}right)=af(x) + bf(y),] where $a,b in mathbb{R}_+$ are fixed positive real numbers, by using direct
Prondanai Kaskasem +2 more
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Characterization, stability and hyperstability of multi-quadratic–cubic mappings
Journal of Inequalities and Applications, 2021 In this paper, we unify the system of functional equations defining a multi-quadratic–cubic mapping to a single equation. Applying a fixed point theorem, we study the generalized Hyers–Ulam stability of multi-quadratic–cubic mappings.
Abasalt Bodaghi, Ajda Fošner
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Two multi-cubic functional equations and some results on the stability in modular spaces
Journal of Inequalities and Applications, 2020 In this article, we study n-variable mappings which are cubic in each variable. We also show that such mappings can be described by an equation, say, multi-cubic functional equation. Furthermore, we study the stability of such functional equations in the
Choonkil Park, Abasalt Bodaghi
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The Mixed Cubic-Quartic Functional Equation
Annals of the Alexandru Ioan Cuza University - Mathematics, 2015 AbstractIn this paper, we obtain the general solution of the following generalized mixed cubic and quartic functional equation f(x + kx) + f(x − ky) = k2{f(x + y) + f(x−y)}−2(k2−1)f(x)−2k2(k2−1)f(y)+ 1/4 k2(k2−1)f(2y), for fixed integers k with k ≠ 0,±1. The Hyers-Ulam stability problem for the mentioned functional equation is also proved.
Bodaghi, A., Kang, D., Rassias, J. M.
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