Fixed points and quadratic rho-functional equations
- Fixed points and quadratic rho-functional equations
- Hyers-Ulam stability; non-Archimedean normed space; fixed point; quadratic rho-functional equation
- Issue Date
- INT SCIENTIFIC RESEARCH PUBLICATIONS
- JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS (2016), v. 9, NO. 4, Page. 1858-1871
- 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 (y)), (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(x + y) + f(x - y) - 2f(x) - 2f (y))
where rho is a fixed non-Archimedean number or a fixed real or complex number with rho not equal -1, 1/2.
Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic rho-functional equations (1) and (2) in non-Archimedean Banach spaces and in Banach spaces. (C) 2016 All rights reserved.
- 2008-1898; 2008-1901
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- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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