Solutions and Stability of Generalized Kannappan's and Van Vleck's Functional Equations

• Autorzy: Elhoucien Elqorachi , Ahmed Redouani
• Języki publikacji: EN

Abstrakty

EN

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, σ is an involutive automorphism of S and µ is a linear combination of Dirac measures ( ᵟ zi)I ∈ I, such that for all i ∈ I, ziis 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. (original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical functions; Functional equation

PL

Matematyka; Funkcje matematyczne; Równanie funkcyjne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2018
• Tom: 32
• Strony: 169--200

Twórcy

autor

Elhoucien Elqorachi

• University Ibn Zohr, Morocco

autor

Ahmed Redouani

• University Ibn Zohr, Morocco

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Identyfikatory

DOI

10.1515/amsil-2017-0006