Additive-Quadratic ρ-Functional Equations in β-Homogeneous Normed Spaces
- Authors
- Lee, Jung Rye; Park, Choonkil; Rassias, Themistocles M.; Yun, Sungsik
- Issue Date
- May-2021
- Publisher
- Springer International Publishing
- Abstract
- Let M1f(x,y):=34f(x+y)−14f(−x−y)+14f(x−y)+14f(y−x)−f(x)−f(y) and M2f(x,y):=2f(x+y2)+f(x−y2)+f(y−x2)−f(x)−f(y). We solve the additive-quadratic ρ-functional inequalities ∥M1f(x,y)∥≤∥ρM2f(x,y)∥, (1) where ρ is a fixed complex number with |ρ|<12, and ∥M2f(x,y)∥≤∥ρM1f(x,y)∥, (2) where ρ is a fixed complex number with |ρ| < 1. Using the direct method, we prove the Hyers–Ulam stability of the additive-quadratic ρ-functional inequalities (1) and (2) in β-homogeneous complex Banach spaces.
- Pages
- 546
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/189389
- DOI
- 10.1007/978-3-030-60622-0_16
- Start Page
- 309
- End Page
- 323
- ISBN
- 978-303060622-0
- ISSN
- 0000-0000
- Files in This Item
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- Appears in
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