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QUADRATIC ρ-FUNCTIONAL EQUATIONS
- Authors
- Lee, Jung Rye; Park, Choonkil; Shin, Dong Yun
- Issue Date
- Sep-2017
- Publisher
- Kluwer Academic Publishers
- Keywords
- Hyers-Ulam stability; non-Archimedean normed space; quadratic rho-functional equation
- Citation
- Journal of Computational Analysis and Applications, v.23, no.3, pp 508 - 520
- Pages
- 13
- Indexed
- SCIE
SCOPUS
- Journal Title
- Journal of Computational Analysis and Applications
- Volume
- 23
- Number
- 3
- Start Page
- 508
- End Page
- 520
- ISSN
- 1521-1398
1572-9206
- Abstract
- In this paper, we solve the quadratic rho-functional equations f (x + y) + f (x - y) - 2f (x) - 2f (y) = rho (2f (x+y/2) + 2f (x -y/2) - f (x) - f (t)), (0.1) where rho is a fixed non-Archimedean number or a fixed real or complex number with rho not equal -1,2, and 2f (x + y/2) + 2f (x - y/2) - f (x) - f(y) = rho(f(x + y) f (x - y) - 2f (x) - 2f (y)), (0.2) where rho is a fixed non-Archimedean number or a fixed real or complex number with rho not equal -1,1/2. Using the direct method, we prove the Hyers-Ulam stability of the quadratic rho-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces and in Banach spaces.
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