The Ulam Type Stability of a Generalized Additive Mapping and Concrete Examples
We give an Ulam type stability result for the following functional equation: f(αx−αx′+x0)=βf(x)−βf(x′)+y0 (for all x,x′∈X) under a suitable condition. We also give a concrete stability result for the case taking up δ∥x∥p∥x′∥q as a control function.
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2013/109754 |
| Summary: | We give an Ulam type stability result for the following functional equation: f(αx−αx′+x0)=βf(x)−βf(x′)+y0 (for all x,x′∈X)
under a suitable condition. We also give a concrete stability result for the case taking up δ∥x∥p∥x′∥q as a control function. |
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| ISSN: | 0161-1712 1687-0425 |