Results 141 to 150 of about 91,298 (162)

Generalized Cauchy difference functional equations

Aequationes mathematicae, 2005
The article concerns primarily the study of functional equations of the form \[ f(x)+ f(y)- f(x+ y)= g(H(x,y)), \] where \(H\) is a given of two (real or complex) variables and where \(f\) and \(g\) are unknown functions. Frist, the author studies the special case \[ f(x)+ f(y)- f(x+ y)= h(\phi(x)+ \phi(y)- \phi(x+y)), \] \(\phi\) analytic, whose ...
openaire   +2 more sources

A Cauchy-like functional equation

aequationes mathematicae, 1998
The author solves the functional equation \[ G(xy-yz)=G(xy-zx)+G(zx-yz)\tag{*} \] for functions \(G\) from the ring of integers into an abelian group, showing that any such function must be a linear combination of four specified functions: the identity function and particular solutions of three simple conditional Cauchy equations.
openaire   +1 more source

A note on an integrated cauchy functional equation

Acta Mathematicae Applicatae Sinica, 1989
The following equation \(f(x)=\int^{\infty}_{0}f(x+y)d\mu (y),\quad a.e.\quad x\geq 0,\) where \(\mu\) is a positive regular Borel measure defined in (0,\(\infty)\), called an integrated Cauchy functional equation, is discussed in order to establish its relevant nonnegative locally integrable solutions in (0,\(\infty)\).
Lau, Kasing, Gu, Huamin
openaire   +2 more sources

Cauchy functional equation problems concerning orthogonality

Aequationes Mathematicae, 2001
This is a survey paper on the conditional Cauchy functional equation of orthogonal additivity. The author discusses its connections with different subjects. Some open problems are presented.
openaire   +1 more source

The Generalized Cauchy Functional Equation

2003
The Cauchy functional equation and the Cauchy-Pexider functional equation are generalized, and their solutions are determined.
openaire   +1 more source

Gleason's theorem and Cauchy's functional equation

International Journal of Theoretical Physics, 1996
The author describes regular and bounded measures on the effect algebra of the closed interval \([0,1]\) (\(a,b \in [0,1]\) are orthogonal iff \(a+b \leq 1\), in this case \(a \oplus b = a+b\) is defined) and shows that every bounded measure is a multiple of the identity.
openaire   +1 more source

Cauchy formula for functional-differential equation

Translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1987, No.5(300), 108- 111 (Russian) (1987; Zbl 0634.34029).
Abdrakhmanov, V. G., Smolin, Yu. N.
openaire   +2 more sources

Cauchy Functional Equation Again

The American Mathematical Monthly, 1978
openaire   +1 more source

Integrated Cauchy Functional Equations on ℝ

1991
RAMACHANDRAN BALASUBRAHMANYAN, KA-SING LAU   +1 more
openaire   +1 more source

Dependence among cauchy-type functional equations

In 1988, Jean Dhombres investigated various kinds of independence among the four forms of the classical Cauchy functional equation as well as solved completely a functional equation, called the universal Cauchy functional equation, which contains all the four forms of the Cauchy functional equation.
openaire   +1 more source