Stability of a Bi-Jensen Functional Equation II
© Kil-Woung Jun et al. 2009
Received: 7 October 2008
Accepted: 24 January 2009
Published: 5 February 2009
Găvruta  provided a further generalization of Rassias' theorem in which he replaced the bound by a general function.
2. Stability of a Bi-Jensen Functional Equation
Jun et al.  established the basic properties of a bi-Jensen mapping in the following lemma.
Now we have the stability of a bi-Jensen mapping.
for all . Then, , and satisfy (2.2), (2.3), (2.4) for all . In addition, satisfy (2.5) for all and also satisfy (2.5) for all . But we get . Hence, the condition is necessary to show that the mapping F is unique.
We have another stability result applying for several cases.
Applying Theorems 2.2–2.7, we easily get the following corollaries.
Applying Theorems 2.6 and 2.7, we obtain the desired result.
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