Stability of additive-quadratic ρ-functional equations in Banach spaces: a fixed point approach
- Authors
- Park, Choonkil; Kim, Sang Og; Alaca, Cihangir
- Issue Date
- Mar-2017
- Publisher
- INT SCIENTIFIC RESEARCH PUBLICATIONS
- Keywords
- Hyers-Ulam stability; additive-quadratic rho-functional equation; fixed point method; Banach space
- Citation
- JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, v.10, no.3, pp.1252 - 1262
- Indexed
- SCIE
- Journal Title
- JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
- Volume
- 10
- Number
- 3
- Start Page
- 1252
- End Page
- 1262
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/152736
- DOI
- 10.22436/jnsa.010.03.34
- ISSN
- 2008-1898
- Abstract
- Let
M(1)f (x, y) : = 3/4 f (x + y) -1/4 f (-x -y) + 1/4 f (x - y) + 1/4 f(y - x) -f (x) -f (y),
M(2)f(x, y) : = 2f( x + y/2) + f ( x - y/2 ) + f ( y - x/2 ) -f (x) -f (y).
We solve the additive-quadratic rho-functional equations
M(1)f (x, y) = rho M(2)f(x, y), (1)
and
M(2)f(x, y) = rho M(1)f (x, y), (2)
where rho is a fixed nonzero number with rho not equal 1.
Using the fixed point method, we prove the Hyers-Ulam stability of the additive-quadratic rho-functional equations (1) and (2) in Banach spaces.
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