QUADRATIC rho-FUNCTIONAL INEQUALITIES IN BANACH SPACES
- Authors
- Park, Choonkil
- Issue Date
- Nov-2015
- Publisher
- SPRINGER
- Keywords
- Hyers-Ulam stability; quadratic rho-functional equation; quadratic rho-functional inequality; complex Banach space
- Citation
- ACTA MATHEMATICA SCIENTIA, v.35, no.6, pp.1501 - 1510
- Indexed
- SCIE
SCOPUS
- Journal Title
- ACTA MATHEMATICA SCIENTIA
- Volume
- 35
- Number
- 6
- Start Page
- 1501
- End Page
- 1510
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/143087
- DOI
- 10.1016/S0252-9602(15)30071-0
- ISSN
- 0252-9602
- Abstract
- In this paper, we solve the quadratic rho-functional inequalities parallel to f(x + y) + f(x - y) - 2f(x) - 2f(y)parallel to <= parallel to rho(2f (x+y/2) + 2f (x - y/2) - f(x) - f(y))parallel to, (0.1) where rho is a fixed complex number with vertical bar rho vertical bar < 1, and parallel to 2f (x + y/2) + 2f(x - y/2) - f(x) - f(y)parallel to <=parallel to rho(f(x + y) + f(x - y) - 2f(x) - 2f(y))parallel to, (0.2) where rho is a fixed complex number with vertical bar rho vertical bar < 1/2. Using the direct method, we prove the Hyers-Ulam stability of the quadratic rho-functional inequalities (0.1) and (0.2) in complex Banach spaces and prove the Hyers-Ulam stability of quadratic rho-functional equations associated with the quadratic rho-functional inequalities (0.1) and (0.2) in complex Banach spaces.
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