@misc{Matkowski_Janusz_Remarks,
author={Matkowski, Janusz},
copyright={Politechnika Poznańska},
howpublished={online},
publisher={Publishing House of Poznan University of Technology},
language={eng},
abstract={The real functions satisfying the inequality Ф (uv) ≤ KФ (u) Ф (v) for some positive K which occur among others in [5], [3], [4], and referred there as submultiplicative, are discussed. A simplifying remark that Ф satisfies this inequality iff KФ is submultiplicative in the standard sense, is done. It is shown that, under general conditions, the standard submultiplicativity of Ф and the inequality Ф (u) Ф (1/u) ≤ 1 imply that Ф must be multi-plicative. Applying a result of Bhatt [1], we observe that if p is a nontrivial seminorm on a Banach algebra X such that the set \{ [formula] .. : ∈ G X, p (x) ≠ 0\} is a singleton \{λ\}, then s = λp is a submultiplicative seminorm on X.},
type={artykuł},
title={Remarks on submultiplicative functions},
keywords={submultiplicativitive function, seminorm, Orlicz function, square property},
}