<abstract xmlns="http://www.w3.org/1999/xhtml"> 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.</abstract>

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.

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

Annales Mathematicae Silesianae

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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;...

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

Data publikacji: 24 sie 2018

Zakres stron: 169 - 200

Otrzymano: 17 lis 2016

Przyjęty: 03 maj 2017

DOI: https://doi.org/10.1515/amsil-2017-0006

Słowa kluczowe
Hyers-Ulam stability, semigroup, d’Alembert’s equation, Van Vleck’s equation, Kannappan’s equation, involution, automorphism, multiplicative function, complex measure

© 2018 Elhoucien Elqorachi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Data publikacji: 24 sie 2018

Zakres stron: 169 - 200

Otrzymano: 17 lis 2016

Przyjęty: 03 maj 2017

DOI: https://doi.org/10.1515/amsil-2017-0006

Słowa kluczoweHyers-Ulam stability, semigroup, d’Alembert’s equation, Van Vleck’s equation, Kannappan’s equation, involution, automorphism, multiplicative function, complex measure

© 2018 Elhoucien Elqorachi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Słowa kluczowe
Hyers-Ulam stability, semigroup, d’Alembert’s equation, Van Vleck’s equation, Kannappan’s equation, involution, automorphism, multiplicative function, complex measure