Abstract
The Ulam-Hyers stability problems of the following quadratic equation r 2 f � x + y r � + r 2 f � x − y r � =2 f(x )+2 f(y), where r is a nonzero rational number, shall be treated. The case r = 2 was introduced by J. M. Rassias in 1999. Furthermore, we prove the stability of the quadratic equation by using the fixed point method. 2010 Mathematics Subject Classification: 39B22; 39B52; 39B72.
Highlights
In 1940, Ulam [1] proposed the general Ulam stability problem
In 1941, this problem was solved by Hyers [2] for the case of Banach spaces
In 1950, Aoki [3] provided a generalization of the Ulam-Hyers stability of mappings by considering variables
Summary
In 1940, Ulam [1] proposed the general Ulam stability problem. In 1941, this problem was solved by Hyers [2] for the case of Banach spaces. It is the first result on the Ulam-Hyers stability of the quadratic functional equation. In 2009, Ravi et al [13] obtained the general solution and the Ulam-Hyers stability of the Euler-Lagrange additive-quadratic-cubic-quartic functional equation f (x + ay) + f (x − ay) = a2f (x + y) + a2f (x − y) + 2(1 − a2)f (x) a4 − a2 +
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