Tomasz Kochanek

Stability problem for number-theoretically multiplicative functions

We deal with the stability question for multiplicative mappings in the sense of number theory. It turns out that the conditional stability assumption: |f(xy) - f(x)f(y)| ≤ e for relatively prime x, y implies that f lies near to some number-theoretically multiplicative function. The domain of f can be general enough to admit, in special cases, the reduction of our result to the well known J. A. Baker - J. Lawrence - F. Zorzitto superstability theorem.

Uncountable sets of unit vectors that are separated by more than 1

Let

THE IDEAL OF WEAKLY COMPACTLY GENERATED OPERATORS ACTING ON A BANACH SPACE

X

Maximal left ideals of the Banach algebra of bounded operators on a Banach space

be a Banach space. We study the circumstances under which there exists an uncountable set

Steinhaus' lattice-point problem for Banach spaces

\mathcal A\subset X

An inconsistency equation involving means

of unit vectors such that

The Szlenk power type and tensor products of Banach spaces

\|x-y\|>1

On a composite functional equation fulfilled by modulus of an additive function

for distinct

Measurable orthogonally additive functions modulo a discrete subgroup

x,y\in \mathcal A

Stability aspects of arithmetic functions, II

. We prove that such a set exists if