Inner product spaces and quadratic functional equations

Advances in Difference Equations

article

Bae, Jae-Hyeong¹  Noori, Batool²  Moghimi, M. B.²  Najati, Abbas² 

[1] Humanitas College, Kyung Hee University;Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili

关键词: Stability;    Quadratic functional equation;    Quadratic function;    Asymptotic behavior;   

DOI  :  10.1186/s13662-021-03307-x

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce the functional equations$$\begin{aligned} f(2x-y)+f(x+2y)&=5\bigl[f(x)+f(y)\bigr], \\ f(2x-y)+f(x+2y)&=5f(x)+4f(y)+f(-y), \\ f(2x-y)+f(x+2y)&=5f(x)+f(2y)+f(-y), \\ f(2x-y)+f(x+2y)&=4\bigl[f(x)+f(y)\bigr]+\bigl[f(-x)+f(-y)\bigr]. \end{aligned}$$We show that these functional equations are quadratic and apply them to characterization of inner product spaces. We also investigate the stability problem on restricted domains. These results are applied to study the asymptotic behaviors of these quadratic functions in complete β-normed spaces.

【 授权许可】

CC BY