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QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN NORMED SPACES
- Authors
- Yun, Sungsik; Park, Choonkil
- Issue Date
- Oct-2016
- Publisher
- Kluwer Academic Publishers
- Keywords
- Hyers-Ulam stability; non-Archimedean normed space; quadratic rho-functional equation; quadratic rho-functional inequality
- Citation
- Journal of Computational Analysis and Applications, v.21, no.4, pp 791 - 799
- Pages
- 9
- Indexed
- SCIE
SCOPUS
- Journal Title
- Journal of Computational Analysis and Applications
- Volume
- 21
- Number
- 4
- Start Page
- 791
- End Page
- 799
- ISSN
- 1521-1398
1572-9206
- 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 (2f (x + y/2) + 2f (x - y/2) - f (x) - f (y))parallel to, (0.1) where rho is a fixed non-Archimedean number with vertical bar rho vertical bar < 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, (0.2) where rho is a fixed non-Archimedean number with vertical bar rho vertical bar < 1/2. Furthermore, we prove the Hyers-Ulam stability of the quadratic rho-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of quadratic rho-functional equations associated with the quadratic rho-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.
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