Opis

• Title:
  Solutions and stability of generalized Kannappan’s and Van Vleck’s functional equations
• Creator:
  Elqorachi, Elhoucien;
  Redouani, Ahmed
• Description:
  We study the solutions of the integral Kannappan’s and Van Vleck’s functional equations∫Sf(xyt)dμ(t) + ∫Sf(xσ(y)t)dμ(t) = 2f(x)f(y), x,y∈S;∫Sf(xσ(y)t)dμ(t) - ∫Sf(xyt)dμ(t) = 2f(x)f(y), x,y∈S,where S is a semigroup, is an involutive automorphism of S and μ is a linear combination of Dirac measures (δz_i)i∈I, such that for all i∈I, zi is in the center of S. We show that the solutions of these equations are closely related to the solutions of the d’Alembert’s classic functional equation with an involutive automorphism. Furthermore, we obtain the superstability theorems for these functional equations in the general case, where σ is an involutive morphism.
• Object availability:
  Dostęp otwarty
• Date:
  2017.08.05
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  angielski
• Source:
  Annales Mathematicae Silesianae; Vol. 32 (2018); 169-200;
  Annales Mathematicae Silesianae; Tom 32 (2018); 169-200;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/13919/10611
• Subject:
  Hyers–Ulam stability;
  semigroup;
  d’Alembert’s equation;
  Van Vleck’s equation;
  Kannappan’s equation;
  involution;
  automorphism;
  multiplicative function;
  complex measure
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/13919
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  poproś o pozwolenie
• Type:
  pozostałe