Results 1 to 10 of about 3,148 (158)

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, Zeglami Driss, Fadli Brahim   +2 more
doaj   +2 more sources

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
doaj   +4 more sources

On a General Conditional Cauchy Functional Equation [PDF]

Sahand Communications in Mathematical Analysis
Let $(G,+)$ 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, Abbas Najati, Yavar Khedmati Yengejeh   +2 more
doaj   +2 more sources

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
doaj   +2 more sources

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.
doaj   +3 more sources

The stability of Cauchy's gamma–beta functional equation

Journal of Mathematical Analysis and Applications, 2004
The authors prove the superstability of the functional equation \[ B(x,y)f(x,y)=f(x)f(y), \] where \(B(x,y)\) is the beta function of Euler and also prove the stability of this equation in the sense of R. Ger.
Lee, Young Whan, Choi, Byung Mun
exaly   +3 more sources

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
doaj   +1 more source

On Stability of the Cauchy Functional Equation in Groupoids [PDF]

Annales Mathematicae Silesianae, 2017
Abstract We give some stability results for the functional equation a(xy) = a(x) + a(y), where a: G → E, G being a groupoid and E a Banach space.
Toborg, Imke, Volkmann, Peter
openaire   +3 more sources

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
doaj   +1 more source

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.
openaire   +2 more sources