Results 1 to 10 of about 3,075 (226)
Alienation of Drygas’ and Cauchy’s Functional Equations [PDF]
Annales Mathematicae Silesianae, 2021 Inspired by the papers [2, 10] we will study, on 2-divisible groups that need not be abelian, the alienation problem between Drygas’ and the exponential Cauchy functional equations, which is expressed by the equation f(x+y)+g(x+y)g(x-y)=f(x)f(y)+2g(x)+g ...
Aissi Youssef +2 more
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Superstability of generalized cauchy functional equations [PDF]
Advances in Difference Equations, 2011 In this paper, we consider the stability of generalized Cauchy functional equations such as Especially interesting is that such equations have the Hyers-Ulam stability or superstability whether g is identically one or not.
Chung Soon-Yeong, Lee Young-Su
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On a General Conditional Cauchy Functional Equation [PDF]
Sahand Communications in Mathematical AnalysisLet $(G,+)$ be an abelian group and $Y$ a linear space over the field $\Bbb{F}\in\{\Bbb{R}, \Bbb{C}\}$. In this paper, we investigate the conditional Cauchy functional equation \[f(x+y)\neq af(x)+bf(y)\quad\Rightarrow \quad f(x+y)=f(x)+f(y),\quad x,y\in
Elham Mohammadi +2 more
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The Cauchy Exponential of Linear Functionals on the Linear Space of Polynomials
Mathematics, 2023 In this paper, we introduce the notion of the Cauchy exponential of a linear functional on the linear space of polynomials in one variable with real or complex coefficients using a functional equation by using the so-called moment equation. It seems that
Francisco Marcellán, Ridha Sfaxi
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Variants of the functional equation of Cauchy
Lietuvos Matematikos Rinkinys, 2004 In this paper solution of the Cauchy functional equation and variants of it are considered.
Juozas Mačys
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Some hyperstability and stability results for the Cauchy and Jensen equations
Journal of Inequalities and Applications, 2022 In this paper we give some hyperstability and stability results for the Cauchy and Jensen functional equations on restricted domains. We provide a simple and short proof for Brzdȩk’s result concerning a hyperstability result for the Cauchy equation.
Mohammad Bagher Moghimi, Abbas Najati
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Gleason-Type Theorems from Cauchy’s Functional Equation [PDF]
Foundations of Physics, 2019 Gleason-type theorems derive the density operator and the Born rule formalism of quantum theory from the measurement postulate, by considering additive functions which assign probabilities to measurement outcomes. Additivity is also the defining property of solutions to Cauchy's functional equation. This observation suggests an alternative proof of the
Victoria J. Wright, Stefan Weigert
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On Cauchy’s functional equation [PDF]
Proceedings of the American Mathematical Society, 1965 for real-valued functions of a real variable. P. Erdos [2] asked, after learning about a preliminary result of S. Hartman [3], whether one obtains all functions satisfying (C) for almost all pairs (x, y) by simply redefining the functions satisfying (C) for all (x, y) in an arbitrary manner on sets of measure zero.
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On Cauchy‐type functional equations
International Journal of Mathematics and Mathematical Sciences, 2004 Let G be a Hausdorff topological locally compact group. Let M(G) denote the Banach algebra of all complex and bounded measures on G. For all integers n ≥ 1 and all μ ∈ M(G), we consider the functional equations , x, y ∈ G, where the functions f, {gi}, {hi}: G → ℂ to be determined are bounded and continuous functions on G.
Elqorachi Elhoucien, Mohamed Akkouchi
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Intuitionistic fuzzy almost Cauchy–Jensen mappings
Demonstratio Mathematica, 2016 In this paper, we first investigate the Hyers–Ulam stability of the generalized Cauchy–Jensen functional equation of p-variable f(∑i=1paixi)=∑i=1paif(xi)$f\left(\sum\nolimits_{i = 1}^p {a_i x_i } \right) = \sum\nolimits_{i = 1}^p {a_i f(x_i )}$ in an ...
Gordji M. E., Abbaszadeh S.
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