QUADRATIC rho-FUNCTIONAL INEQUALITIES IN BANACH SPACES: A FIXED POINT APPROACH
- Authors
- Park, Choonkil; Seo, Jeong Pil
- Issue Date
- Jun-2015
- Publisher
- KANGWON-KYUNGKI MATHEMATICAL SOC
- Keywords
- Hyers-Ulam stability; quadratic $; rho$-functional equation; fixed point; complex Banach space
- Citation
- KOREAN JOURNAL OF MATHEMATICS, v.23, no.2, pp.231 - 248
- Indexed
- KCI
- Journal Title
- KOREAN JOURNAL OF MATHEMATICS
- Volume
- 23
- Number
- 2
- Start Page
- 231
- End Page
- 248
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/143471
- DOI
- 10.11568/kjm.2015.23.2.231
- ISSN
- 1976-8605
- Abstract
- In this paper, we solve the following quadratic rho-functional inequalities parallel to f (x+y+z/2) + f (x-y-z/2) + f(y-x-z/2) + f (z-x-y/2) - f (x) - f (y) - f (z) parallel to (0.1) <= parallel to rho(f (x+y+x) + f (x-y-z) + f (y-x-z) +f (z-x-y) - 4f (x) - 4f (y) - 4f(z)) parallel to, where rho is a fi xed complex number with |rho| < 1/8, and parallel to rho(f (x+y+x) + f (x-y-z) + f (y-x-z) +f (z-x-y) - 4f (x) - 4f (y) - 4f(z)) parallel to (0.2) <= parallel to f (x+y+z/2) + f (x-y-z/2) + f(y-x-z/2) + f (z-x-y/2) - f (x) - f (y) - f (z) parallel to, where rho is a fixed complex number with |rho| < 4. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic rho-functional inequalities (0.1) and (0.2) in complex Banach spaces.
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