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Fixed points and additive ρ-functional equations
- Authors
- Park, Choonkil; Shin, Dong Yun; Lee, Jung Rye
- Issue Date
- Sep-2016
- Publisher
- Birkhauser Verlag
- Keywords
- Hyers-Ulam stability; additive rho-functional equation; fixed point; non-Archimedean normed space; Banach space
- Citation
- Journal of Fixed Point Theory and Applications, v.18, no.3, pp 569 - 586
- Pages
- 18
- Indexed
- SCIE
SCOPUS
- Journal Title
- Journal of Fixed Point Theory and Applications
- Volume
- 18
- Number
- 3
- Start Page
- 569
- End Page
- 586
- ISSN
- 1661-7746
1661-7746
- Abstract
- In this paper, we solve the additive rho-functional equations f(x + y) - f(x) - f(y) = rho(2f(x+y/2) - f(x) - f(y)), 2f(x+y/2) - f(x) - f(y) = rho(f(x+y) - f(x) - f(y)), where rho is a fixed non-Archimedean number or a fixed real or complex number with rho not equal 1. Using the fixed point method, we prove the Hyers-Ulam stability of the above additive rho-functional equations in non-Archimedean Banach spaces and in Banach spaces.
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