Results 311 to 320 of about 3,258,064 (367)

On stability of the Cauchy equation on semigroups

Aequationes Mathematicae, 1988
We say that Hyers's theorem holds for the class of all complex-valued functions defined on a semigroup (S, +) (not necessarily commutative) if for anyf:S → ℂ such that the set {f(x + y) − f(x) − f(y): x, y ∈ S} is bounded, there exists an additive functiona:S → ℂ for which the functionf − a is bounded.
Z. Gajda
semanticscholar   +3 more sources

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On the Euler--Cauchy Equation

The American Mathematical Monthly, 1961
B. Schweizer
semanticscholar   +3 more sources

The Cauchy equation on I-semigroups

Aequationes Mathematicae, 2002
We give the general solution of the Cauchy equation on a general I-semigroup, i.e. in a given interval $ [0, M] \subset \overline{\mathbb{R}}^+ $ with a pseudo-addition $ \oplus $ . Then we present some examples of solutions.
Pietro Benvenuti, D. Vivona, M. Divari
semanticscholar   +4 more sources

On an alternative functional equation related to the Cauchy equation

Aequationes Mathematicae, 1982
We consider the following problem: Let (G, +) be an abelian group,B a complex Banach space,a, b∈B,b≠0,M a positive integer; find all functionsf:G →B such that for every (x, y) ∈G ×G the Cauchy differencef(x+y)−f(x)−f(y) belongs to the set {a, a+b, a+2b, ...,a+Mb}.
G. Forti
semanticscholar   +3 more sources

An analytic study on the approximate solution of a nonlinear time‐fractional Cauchy reaction–diffusion equation with the Mittag–Leffler law

Mathematical methods in the applied sciences, 2021
The main aim of the current article is considering a nonlinear time‐fractional Cauchy reaction–diffusion equation with the Mittag–Leffler law and deriving its approximate analytical solution in a systematic way.
K. Hosseini, M. Ilie, M. Mirzazadeh, D. Baleanu   +3 more
semanticscholar   +1 more source

On Cauchy’s Equations of Motion

Zeitschrift für angewandte Mathematik und Physik ZAMP, 1964
Cauchys Bewegungs- und Momentengleichungen der klassischen Kontinuumsmechanik werden, mit Hilfe von Invarianz-Bedingungen gegenuber starren Zusatzbewegungen, aus dem Energietheorem hergeleitet.
Ronald S. Rivlin, A. E. Green
openaire   +2 more sources

The solution of Euler-Cauchy equation using Laplace transform

, 2015
Euler-Cauchy equation is a typical example of ODE with variable coefficients. Since this equation has a simple form, we would like to start from this equation to find the solution of ODEs with variable coefficients.
B. Ghil, Hwajoon Kim
semanticscholar   +1 more source

ON APPROXIMATE CAUCHY EQUATION IN FELBIN'S TYPE FUZZY NORMED LINEAR SPACES

, 2013
In this paper we study the Hyers-Ulam-Rassias stability of Cauchy equation in Felbin's type fuzzy normed linear spaces. As a result we give an example of a fuzzy normed linear space such that the fuzzy version of the stability problem remains true, while
I. Sadeqi, F. Moradlou, M. Salehi
semanticscholar   +1 more source

FRACTIONAL QUANTUM EULER–CAUCHY EQUATION IN THE SCHRÖDINGER PICTURE, COMPLEXIFIED HARMONIC OSCILLATORS AND EMERGENCE OF COMPLEXIFIED LAGRANGIAN AND HAMILTONIAN DYNAMICS

, 2009
Fractional quantum Euler–Cauchy equation in the Schrodinger picture is derived from the fractional action-like variational approach recently introduced by the author. Many interesting consequences are revealed and explored, in particular the emergence of
A. R. El-Nabulsi
semanticscholar   +1 more source

Cauchy Equation on Discrete Domain and Some Characterization Theorems

, 1994
Discrete version of normal distribution, i.e., $P(x) = c\exp \{ - \beta x^2 \} , \beta > 0, x \in {\bf Z}$, is characterized via the solution of Cauchy type equation on discrete domain in dimension 4 or higher. It is also shown that this characterization
R. Dasgupta
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