Fixed Points and Quadratic rho-Functional Inequalities in Banach Spaces
- Authors
- Lu, Gang; Kim, Gwang Hui; Park, Choonkil
- Issue Date
- Dec-2020
- Publisher
- CHIANG MAI UNIV, FAC SCIENCE
- Keywords
- Hyers-Ulam stability; quadratic rho-functional inequality; fixed point; Banach space
- Citation
- THAI JOURNAL OF MATHEMATICS, v.18, no.4, pp.1733 - 1742
- Indexed
- SCOPUS
- Journal Title
- THAI JOURNAL OF MATHEMATICS
- Volume
- 18
- Number
- 4
- Start Page
- 1733
- End Page
- 1742
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/144247
- ISSN
- 1686-0209
- 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(4f(x+y/2) + f(x - y) - 2f(x) - 2f(y))parallel to,
where rho is a fixed number with vertical bar rho vertical bar < 1, and
parallel to 4f(x + y/2) + f(x - y) - 2f(x) - 2f(y)parallel to <= parallel to rho(f(x + y) + f(x - y) - 2f(x) -2f(y))parallel to,
where rho is a fixed number with vertical bar rho vertical bar < 1/2. Using the fixed point method, we prove the Hyers-Ulam stability of the above quadratic rho-functional inequalities in complex Banach spaces.
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