Additive functional equation and inequality are stable in Banach space and its applications
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DOI:
https://doi.org/10.26637/mjm101/002Abstract
In this paper, the authors established the solution of the additive functional equation and inequality
$$
f(x)+f(y+z)-f(x+y)=f(z)
$$
and
$$
\|f(x)+f(y+z)-f(x+y)\| \leq\|f(z)\| .
$$
We also prove that the above functional equation and inequality are stable in Banach space in the sense of Ulam, Hyers, Rassias. An application of this functional equation is also studied.
Keywords:
Additive functional equations, generalized Hyers - Ulam - Rassias stabilityMathematics Subject Classification:
39B52, 32B72, 32B82- Pages: 10-17
- Date Published: 01-01-2013
- Vol. 1 No. 01 (2013): Malaya Journal of Matematik (MJM)
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