Description

• Title:
  On some conditional functional equations
• Creator:
  Szostok, Tomasz
• Description:
  Let X, Y be real linear spaces. We are looking for a function G : X2→ℝ such that the equationf(x+y) = G(x,y)[f(x)+f(y)]is equivalent to the orthogonal Cauchy equationx⟂y ⇒ f(x+y)=f(x)+f(y).Several kinds of orthogonalities are considered. The quotient ‖(x-y)/(x+y)‖ closely connected with the James orthogonality plays here a distinguished role. Similar problems are considered for the Ptolemaic equationx⟂y ⇒ f(x+y)f(x-y) = f(x)2+f(y)2.As a result a characterization of inner product spaces is obtained.
• Object availability:
  free access
• Date:
  2003.01.30
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol 16 (2002); 65-77;
  Annales Mathematicae Silesianae; Tom 16 (2002); 65-77;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/14109/10833
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/14109
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  seek permission
• Type:
  other