Stability of Bi-additive s-Functional Inequalities and Quasi-multipliers
- Authors
- Lee, Jung Rye; Park, Choonkil; Rassias, Themistocles M.; Yun, Sungsik
- Issue Date
- May-2021
- Publisher
- Springer
- Abstract
- Park et al. (Rocky Mt J Math 49, 593–607 (2019)) solved the following bi-additive s-functional inequalities: ∥f(x+y,z−w)+f(x−y,z+w)−2f(x,z)+2f(y,w)∥≤∥∥s(2f(x+y2,z−w)+2f(x−y2,z+w)−2f(x,z)+2f(y,w))∥∥, (1) ∥∥2f(x+y2,z−w)+2f(x−y2,z+w)−2f(x,z)+2f(y,w)∥∥≤∥s(f(x+y,z−w)+f(x−y,z+w)−2f(x,z)+2f(y,w))∥, (2) where s is a fixed nonzero complex number with |s| < 1. Using the direct method, we prove the Hyers–Ulam stability of quasi-multipliers on Banach algebras, associated with the bi-additive s-functional inequalities (1) and (2).
- Pages
- 546
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/189390
- DOI
- 10.1007/978-3-030-60622-0_17
- Start Page
- 325
- End Page
- 337
- ISBN
- 978-303060622-0
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