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Additive rho-functional inequalities
- Authors
- Park, Choonkil
- Issue Date
- Oct-2014
- Publisher
- International Scientific Research Publications
- Keywords
- Hyers-Ulam stability; additive rho-functional equation; additive rho-functional inequality; non-Archimedean normed space; Banach space
- Citation
- Journal of Nonlinear Science and Applications, v.7, no.5, pp 296 - 310
- Pages
- 15
- Indexed
- SCIE
- Journal Title
- Journal of Nonlinear Science and Applications
- Volume
- 7
- Number
- 5
- Start Page
- 296
- End Page
- 310
- ISSN
- 2008-1898
2008-1901
- Abstract
- In this paper, we solve the additive rho-functional inequalities parallel to f(x + y) - f(x) - f(y)parallel to <= parallel to rho(2f(x+ y/2) - f(x) - f(y))parallel to, (1) parallel to 2f(x + y/2) - f(x) - f(y)parallel to <= parallel to rho(f(x + y) - f(x) - f(y))parallel to, (2) where rho is a fixed non-Archimedean number with vertical bar rho vertical bar < 1 or rho is a fixed complex number with vertical bar rho vertical bar < 1. Using the direct method, we prove the Hyers-Ulam stability of the additive rho-functional inequalities (I) and (2) in non-Archimedean Banach spaces and in complex Banach spaces, and prove the Hyers-Ulam stability of additive rho-functional equations associated with the additive rho-functional inequalities (1) and (2) in non-Archimedean Banach spaces and in complex Banach spaces.
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