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Cauchy's functional equation in restricted complex domains [PDF]

International Journal of Mathematics and Mathematical Sciences, 2006
Using a method modified from that used by Pisot and Schoenberg in 1964-1965, a Cauchy's functional equation with restricted domains in the complex field is solved for uniformly continuous solutions.
Watcharapon Pimsert, Vichian Laohakosol, Sajee Pianskool   +2 more
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Alienation of Drygas’ and Cauchy’s Functional Equations [PDF]

Annales Mathematicae Silesianae, 2021
Abstract 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
Youssef Aissi, Driss Zeglami, B. Fadli
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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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Superstability of generalized cauchy functional equations [PDF]

Advances in Difference Equations, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chung Soon-Yeong, Lee Young-Su
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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 the stability of the squares of some functional equations

Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2015
We consider the stability, the superstability and the inverse stability of the functional equations with squares of Cauchy’s, of Jensen’s and of isometry equations and the stability in Ulam-Hyers sense of the alternation of functional equations and of ...
Zenon Moszner
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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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Power series expansions of arbitrary order functional difference equations [PDF]

Notes on Number Theory and Discrete Mathematics
This paper looks at some real and complex generalizations of power series associated with some arbitrary order functional difference equations considered as generalizations and extensions of Fibonacci and Lucas numbers.
Anthony G. Shannon, Omür Deveci, Özgür Erdağ   +2 more
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Rings all of whose additive group endomorphisms are left multiplications

International Journal of Mathematics and Mathematical Sciences, 1984
Motivated by Cauchy's functional equation f(x+y)=f(x)+f(y), we study in §1 special rings, namely, rings for which every endomorphism f of their additive group is of the form f(x)≡ax. In §2 we generalize to R algebras (R a fixed commutative ring) and give
Michael I. Rosen, Oved shisha
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