Alienation of the Jensen, Cauchy And D'alembert Equations

• Autorzy: Barbara Sobek
• Języki publikacji: EN

Abstrakty

EN

Let (S, +) be a commutative semigroup, c : S S be an endomorphism with c2 = id and let K be a field of characteristic different from 2. Inspired by the problem of strong alienation of the Jensen equation and the exponential Cauchy equation, we study the solutions f, g : S K of the functional equation f (x + y) + f (x + c(y)) + g(x + y) = 2f (x) + g(x)g(y) for x, y e S. We also consider an analogous problem for the Jensen and the d'Alembert equations as well as for the d'Alembert and the exponential Cauchy equations.(original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical analysis; Mathematical functions; Functional equation

PL

Matematyka; Analiza matematyczna; Funkcje matematyczne; Równanie funkcyjne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2016
• Tom: 30
• Strony: 181--191

Twórcy

autor

Barbara Sobek

• University of Rzeszów, Poland

Bibliografia

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Identyfikatory

DOI

10.1515/amsil-2016-0007