Description

• Title:
  On a functional equation appearing on the margins of a mean invariance problem
• Creator:
  Jarczyk, Justyna;
  Jarczyk, Witold
• Description:
  Given a continuous strictly monotonic real-valued function α, defined on an interval I, and a function ω:I→(0,+∞) we denote by Bωα the Bajraktarević mean generated by α and weighted by ω:Bωα(x,y) = α-1(\frac{ω(x)}{ω(x)+ω(y)}α(x) + \frac{ω(y)}{ω(x)+ω(y)}α(y)), x,y∈I.We find a necessary integral formula for all possible three times differentiable solutions (ϕ,ψ) of the functional equationr(x)Bsϕ(x,y) + r(y)Btψ{t}(x,y) = r(x)x + r(y)y,where r, s,t:I→(0,+∞) are three times differentiable functions and the first derivatives of ϕ,ψ and r do not vanish. However, we show that not every pair (ϕ,ψ) given by the found formula actually satisfies the above equation.
• Object availability:
  free access
• Date:
  2020.07.09
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol 34 No 1 (2020); 96-103;
  Annales Mathematicae Silesianae; Tom 34 Nr 1 (2020); 96-103;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/13635/10441
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/13635
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  seek permission
• Type:
  other