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2015 | 29 | 61--83
Tytuł artykułu

Inequalities of Lipschitz Type for Power Series in Banach Algebras

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let f (z) = P1 n=0 ********nzn be a function defined by power series with complex coefficients and convergent on the open disk D(0;R) ******** C, R > 0: For any x; y 2 B, a Banach algebra, with kxk ; kyk < R we show among others that kf (y) f (x)k ******** ky xk Z 1 0 f0a (k(1 t) x + tyk) dt where fa (z) = P1 n=0 j********nj zn: Inequalities for the commutator such as kf (x) f (y) f (y) f (x)k ******** 2fa (M) f0a (M) ky xk ; if kxk ; kyk ******** M < R; as well as some inequalities of Hermite-Hadamard type are also provided.(original abstract)
Rocznik
Tom
29
Strony
61--83
Opis fizyczny
Twórcy
  • Mathematics, School of Engineering & Science Victoria University
Bibliografia
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
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