Opis

• Title:
  Addition formulae with singularities
• Creator:
  Domańska, Katarzyna;
  Ger, Roman
• Description:
  We deal with functional equations of the formf(x+y) = F(f(x),f(y))(so called addition formulas) assuming that the given binary operation F is associative but its domain of definition is disconnected (admits "singularities"). The functionFlu,v) := (u+v)/(1+uv)serves here as a good example; the corresponding equation characterizes the hyperbolic tangent. Our considerations may be viewed as counterparts of L. Losonczi's [4] and K. Domańska's [2] results on local solutions of the functional equationf(F(x,y)) = f(x) + f(y)with the same behaviour of the given associative operation F.Our results exhibit a crucial role of 1 that turns out to be the critical value towards the range of the unknown function. What concerns the domain we admit fairly general structures (groupoids, groups, 2-divisible groups). In the case where the domain forms a group admitting subgroups of index 2 the family of solutions enlarges considerably.
• Object availability:
  Dostęp otwarty
• Date:
  2004.09.30
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  angielski
• Source:
  Annales Mathematicae Silesianae; Vol. 18 (2004); 7-20;
  Annales Mathematicae Silesianae; Tom 18 (2004); 7-20;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/14088/10807
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/14088
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  poproś o pozwolenie
• Type:
  pozostałe