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## CURRENTLY DISPLAYING:

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## Cauchy—Kovalevskaya theory for equations with deviating variables

### Aequationes Mathematicae (1999-08-01) 58: 143-156 , August 01, 1999

### Summary.

We prove existence theorems of the Cauchy—Kovalevskaya type for linear partial differential equations with deviating variables. Our results generalize to strongly coupled systems and equations with deviations dependent on the unknown function. We give also sufficient conditions for a nontrivial case where the deviations depend on the unknown function.

## Subdirectly irreducible algebras with various equations

### Aequationes Mathematicae (2004-08-01) 68: 98-107 , August 01, 2004

### Summary.

In this paper we characterize subdirectly irreducible algebras with various equations, the main part of which are hyperidentities and hyperquasiidentities.

## On the stability of Wright-convex functions

### Aequationes Mathematicae (2003-02-01) 65: 158-164 , February 01, 2003

### Summary.

We show that if *D* is an open and convex subset of
$ \mathbb{R}^N $
and
$ f: D \to \mathbb{R} $
fulfils the inequality¶¶
$ f(tx + (1 - t)y) + f((1 - t)x+ty) \le f(x) + f(y) + 2\delta, \qquad x,y \in D, \quad t \in [0,1], \eqno{(\ast)} $
¶¶ where
$ \delta \ge 0 $
is a given constant, then there exists a Wright-convex function
$ g : D \to \mathbb{R} $
(i.e. *g* satisfies condition (*) for all
$ x,y \in D $
and
$ t \in [0,1] $
with
$ \delta = 0) $
such that¶¶
$ \mid f(x) - g(x)\mid \le \theta\cdot\delta,\qquad x \in D, $
¶¶ where
$ \theta $
is a constant depending only on the dimension *N*.

## On an axiomatization of the quasi-arithmetic mean values without the symmetry axiom

### Aequationes Mathematicae (2000-02-01) 59: 74-83 , February 01, 2000

### Summary.

Kolmogoroff and Nagumo proved that the quasi-arithmetic means correspond exactly to the decomposable sequences of continuous, symmetric, strictly increasing in each variable and reflexive functions. We replace decomposability and symmetry in this characterization by a generalization of the decomposability.

## Personal reflections on an unintentional behavioral scientist

### Aequationes Mathematicae (1999-08-01) 58: 3-15 , August 01, 1999

### Summary.

This article consists of some personal reflections on aspects of János Aczél's role in the development of mathematical behavioral and social sciences; it is not a new contribution to the literature on functional equations, but rather a recounting of some history.

## On spines of Seifert fibered manifolds

### Aequationes Mathematicae (2003-02-01) 65: 40-60 , February 01, 2003

### Summary.

We define a family of balanced presentations of groups and prove that they correspond to spines of some Seifert fibered 3-manifolds. These presentations of groups (and manifolds) generalize in a natural way many classes of presentations of groups (and manifolds) previously studied by several authors. Moreover, we construct crystallizations representing the small Seifert manifolds of the considered class.

## The Forty-first International Symposium on Functional Equations, June 8-15, 2003, Noszvaj, Hungary

### Aequationes Mathematicae (2004-06-01) 67: 285-320 , June 01, 2004

## Linear functional equations and their Baire category properties

### Aequationes Mathematicae (2000-11-01) 60: 315-320 , November 01, 2000

### Summary.

The paper contains some qualitative considerations, both from topological and measure-theoretical points of view, concerning the set of linear functional equations.

## Topological transitivity for expanding piecewise monotonic maps on the interval

### Aequationes Mathematicae (1999-05-01) 57: 303-311 , May 01, 1999

### Summary.

Let *T* : [0, 1] → [0, 1] be an expanding piecewise monotonic map. Conditions on *T* and
$ {\rm inf}_{x\in [0,1]}|T^{\prime}x| $
implying the topological transitivity of *T* are investigated. For a monotonic mod one transformation *T* topological transitivity is obtained, if
$ {\rm inf}_{x\in [0,1]}|T^{\prime}x| > 2 $
. If *T* is a monotonic mod one transformation with three monotonic pieces, then
$ {\rm inf}_{x\in [0,1]}|T^{\prime}x| \geq 2 $
implies the topological transitivity of *T*. An expanding monotonic mod one transformation *T* with lim_{x}_{→ 0}+ *T x* = 0 or lim_{x}_{→ 1} - *T x* = 1 is topologically transitive.

## A convolution inequality

### Aequationes Mathematicae (1999-05-01) 57: 185-200 , May 01, 1999

### Summary.

We show that every nonnegative measurable solution of the convolution inequality¶¶
$$\phi (t)\ge \int_E^{}\phi (t+s)d\mu (s),\qquad t \in E, $$
¶(where *E* is a closed additive subgroup of *R* and μ a suitable measure) is equal almost everywhere to an exponential function.