On the best Hyers-Ulam stability constants for some equations and operators. (English) Zbl 1378.39019
Pardalos, Panos M. (ed.) et al., Contributions in mathematics and engineering. In honor of Constantin Carathéodory. With a foreword by R. Tyrrell Rockafellar. Cham: Springer (ISBN 978-3-319-31315-3/hbk; 978-3-319-31317-7/ebook). 517-528 (2016).
Let \(X\) be a normed space and let \(Y\) be a Banach space over \(\mathbb{R}\) and \(f:X\to Y\) be an unknown map. In this paper, the authors review some existing results based on D. Popa and I. Rasa [Expo. Math. 31, No. 3, 205–214 (2013; Zbl 1284.39032); J. Math. Anal. Appl. 412, No. 1, 103–108 (2014; Zbl 1308.41026)] on the best constant in Hyers-Ulam stability of the classical functional equations: Cauchy, Jensen, and quadratic equations, i.e., \(f(x+y)=f (x)+f(y)\), \(f(\frac{x+y}{2})=\frac{f(x)+f(y)}{2}\), \(f(x+y)+f(x-y)=2f(x)+2f(y)\), respectively.
For the entire collection see [Zbl 1355.00026].
For the entire collection see [Zbl 1355.00026].
Reviewer: Maryam Amyari (Mashhad)
MSC:
| 39B82 | Stability, separation, extension, and related topics for functional equations |
| 39B52 | Functional equations for functions with more general domains and/or ranges |
