ADDITIVE-QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN β-HOMOGENEOUS NORMED SPACES
- Authors
- Yun, Sungsik; Anastassiou, George A.; Park, Choonkil
- Issue Date
- Nov-2016
- Publisher
- EUDOXUS PRESS, LLC
- Keywords
- Hyers-Ulam stability; beta-homogeneous space; additive-quadratic rho-functional equation; additive-quadratic rho-functional inequality
- Citation
- JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, v.21, no.5, pp.897 - 909
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
- Volume
- 21
- Number
- 5
- Start Page
- 897
- End Page
- 909
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/153608
- ISSN
- 1521-1398
- Abstract
- In this paper, we solve the following additive-quadratic p-functional inequalities
parallel to f(x + y) + f(x - y) - 2f(x) - f(y) - f(-y)parallel to (0.1)
<= parallel to rho(2f (x + y/2) +2f (x - y/2) -3/2f(x) + 1/2f(x) -1/2f(y) - 1/2f(-y))parallel to,
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) - 3/2f(x) + 1/2f(-x) - 1/2f(y) - 1/2f(-y)parallel to
<=parallel to p(f(x + y) + f(x - y)- 2f(x) - f(y) - f(-y))parallel to,
where rho is a fixed complex number with vertical bar rho vertical bar < 1/2-, and prove the Hyers-Ulam stability of the additive quadratic rho-functional inequalities (0.1) and (0.2) in beta-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of additive-quadratic rho-functional equations associated with the additive-quadratic rho-functional inequalities (0.1) and (0.2) in beta-homogeneous complex Banach spaces.
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