Asymptotic behavior of Fréchet functional equation and some characterizations of inner product spaces

• Autorzy: Park Choonkil , Tareeghee Mohammad Amin , Najati Abbas , Yengejeh Yavar Khedmati , Paokanta Siriluk

Identyfikatory

DOI

10.1515/dema-2023-0265

• Języki publikacji: EN

Abstrakty

EN

This article presents the general solution f: G→V of the following functional equation: f(x)−4f(x+y)+6f(x+2y)−4f(x+3y)+f(x+4y)=0,x,y∈G, where (G,+) is an abelian group and V is a linear space.We also investigate its Hyers-Ulam stability on some restricted domains. We apply the obtained results to present some asymptotic behaviors of this functional equation in the framework of normed spaces. Finally, we provide some characterizations of inner product spaces associated with the mentioned functional equation.

Słowa kluczowe

EN

Hyers-Ulam stability; quadratic function; cubic function; Fréchet functional equation; asymptotic behavior

PL

stabilność Hyersa-Ulama; funkcja kwadratowa; funkcja sześcienna; równanie funkcyjne Frécheta; zachowanie asymptotyczne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20230265
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Park Choonkil

• Department of Mathematics, Hanyang University, Seoul, Korea

autor

Tareeghee Mohammad Amin

• Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

autor

Najati Abbas

• Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

autor

Yengejeh Yavar Khedmati

• Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

autor

Paokanta Siriluk

• School of Science, University of Phayao, Phayao 56000, Thailand

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).