Szukana fraza: [Abstrakt = "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."]

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