On several occasions in investigations of functional equations it has been observed that the
family of the solutions of the equation in question depends quite essentially on the domain in …

1. Let (G,+),(#,+) and (R,+,•) be two abelian groups and an integral domain, respectively. In
the sequel, unless explicitly stated otherwise, the letter/will denote a map of G into R or G …

Roman Ger Department of Mathematics Silesian University 40-007 Ka.towice ABSTRACT.
Answering a question of L. Reich, we here pre Page 1 AlMOST APPROXIMATELY ADDITIVE …

A. Karasińska, E. Wagner-Bojakowska MICROSCOPIC AND STRONGLY MICROSCOPIC
SETS ON THE PLANE. FUBINI THEOREM AND FUBINI PROPERTY Page 1 DEMONSTRATIO …

We consider variants on the classical Berz sublinearity theorem, using only DC, the Axiom of
Dependent Choices, rather than AC, the Axiom of Choice, which Berz used. We consider …

In this paper we deal with the extension of the following functional equation¶¶
f(x)=M\bigl(f(m_1(x,y)),\dots,f(m_k(x,y))\bigr)\qquad(x,y∈K),(*)¶ where M is ak-variable …

The Olkin–Baker functional equation, except of being studied inside the theory of functional
equations, is closely related to the celebrated Lukacs characterization of the gamma …

We describe various types of approximate solutions and stability results for the Wigner
equation in Hilbert spaces. Presented results cover, among others, the generalized Hyers …

For inner product spaces X and Y, we consider the orthogonality equation (f (x)| f (z))=(x| z)
for x, z∈ X as well as its restricted versions (f (x)| f (z))=(x| z) for (x, z)∈ X2\M and (f (x)| f …

We generalize the well-known result of R. Ger (see 6) on almost additive functions, ie we
prove the following¶¶ Theorem. Let S be a left reversible semigroup and let \calI be a left …