Description

• Title:
  A generalized a-Wright convexity and related functional equation
• Creator:
  Matkowski, Janusz;
  Wróbel, Małgorzata
• Description:
  Let I be an interval and M,N: I×I→I some means with the strict internality property. Suppose that ϕ: I→ℝ is a non-constant and continuous solution of the functional equationϕ(M(x,y)) + ϕ(N(x,y)) = ϕ(x) + ϕ(y).Then ϕ is one-to-one; moreover for every lower semicontinuous function f: I→ℝ satisfying the inequalityf(M(x,y)) + f(N(x,y)) ≤ f(x) + f(y),the function f◦ϕ-1 is convex on ϕ(I). This is a generalization of an earlier result of Zs. Páles. An application to the a-Wright convex function is given.
• Object availability:
  free access
• Date:
  1996.09.30
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol. 10 (1996); 7-12;
  Annales Mathematicae Silesianae; Tom 10 (1996); 7-12;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/14188/10915
• Subject:
  a-Wright convexity;
  Jensen convexity;
  semicontinuity;
  functional equation;
  functional inequality
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/14188
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  seek permission
• Type:
  other