Quadratic ρ-functional inequalities in complex matrix normed spaces
- Authors
- Wang, Zhihua; Park, Choonkil
- Issue Date
- 2016
- Publisher
- INT SCIENTIFIC RESEARCH PUBLICATIONS
- Keywords
- Hyers-Ulam stability; matrix normed space; quadratic rho-functional equation; quadratic rho-functional inequality
- Citation
- JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, v.9, no.9, pp.5344 - 5352
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
- Volume
- 9
- Number
- 9
- Start Page
- 5344
- End Page
- 5352
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/155522
- DOI
- 10.22436/jnsa.009.09.03
- ISSN
- 2008-1898
- Abstract
- In this paper, we solve the following 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,
where rho is a fixed complex number with |rho| < 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,
where rho is a fixed complex number with |rho| < 1/2. By using the direct method, we prove the Hyers-Ulam stability of these inequalities in complex matrix normed spaces, and prove the Hyers-Ulam stability of quadratic rho-functional equations associated with these inequalities in complex matrix normed spaces.
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