Description

• Title:
  Inequalities of Lipschitz type for power series in Banach algebras
• Creator:
  Dragomir, Sever S.
• Description:
  Let f(z) = Σn=0∞αnzn 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∈𝓑, a Banach algebra, with ‖x‖,‖y‖<R we show among others that‖f(y)-f(x)‖ ≤ ‖y-x‖∫01f'a(‖(1-t)x+ty‖)dtwhere fa(z) = Σn=0∞|αn|zn. Inequalities for the commutator such as‖f(x)f(y) - f(y)f(x)‖ ≤ 2fa(M)f'a(M)‖y-x‖,if ‖x‖,‖y‖≤M<R, as well as some inequalities of Hermite–Hadamard type are also provided.
• Object availability:
  free access
• Date:
  2015.09.30
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol 29 (2015); 61-83;
  Annales Mathematicae Silesianae; Tom 29 (2015); 61-83;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/13978/10678
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/13978
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  seek permission
• Type:
  other