Hyers-Ulam stability; quadratic α-functional equation; fixed point method; direct method; Banach space
INT SCIENTIFIC RESEARCH PUBLICATIONS
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, v. 9, NO 6, Page. 3980-3991
In this paper, we investigate the quadratic alpha-functional equation
2f (x) + 2 f (y) - f (x y) + alpha(-2) f (alpha(x + y)), (1)
2f (x) + 2f (y) = f (x + y) + alpha(-2) f (alpha(x-y)), (2)
where alpha is a fixed nonzero real or complex number with alpha(-1) not equal +/-root 3.
Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic alpha-functional equations (1) and (2) in Banach spaces. (C) 2016 All rights reserved.