Alienation of the Jensen, Cauchy and d’Alembert Equations

• Autorzy: Barbara Sobek
• Języki publikacji: EN

Abstrakty

EN

Let (S, +) be a commutative semigroup, σ : S → S be an endomorphism with σ2 = 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+σ(y))+g(x+y)=2f(x)+g(x)g(y)     for  x,y∈S. $$f(x + y) + f(x + \sigma (y)) + g(x + y) = 2f(x) + g(x)g(y)\;\;\;\;{\rm for}\;\;x,y \in S.$$ 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.

Słowa kluczowe

EN

Alienation; exponential Cauchy equation; Jensen equation; d’Alembert equation

Kategorie tematyczne

• 39B52: Equations for functions with more general domains and/or ranges
• 39B72: Systems of functional equations and inequalities

• Wydawca: De Gruyter Open
• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2016
• Tom: 30
• Numer: 1
• Strony: 181-191

Daty

wydano

2016-09-01

otrzymano

2016-04-01

poprawiono

2016-05-20

zaakceptowano

2016-05-21

online

2016-09-23

Twórcy

autor

Barbara Sobek

• Faculty of Mathematics and Natural Sciences, University of Rzeszów, Pigonia 1, 35-310 Rzeszów,

Identyfikatory

DOI

10.1515/amsil-2016-0007