Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces
We obtain the general solution of the generalized mixed additive and quadratic functional equation fx+my+fx−my=2fx−2m2fy+m2f2y, m is even; fx+y+fx−y−2m2−1fy+m2−1f2y, m is odd, for a positive integer m. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spa...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/198018 |
| Summary: | We obtain the general solution of the generalized mixed additive and quadratic functional equation fx+my+fx−my=2fx−2m2fy+m2f2y, m is even; fx+y+fx−y−2m2−1fy+m2−1f2y, m is odd, for a positive integer m. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces when m is an even positive integer or m=3. |
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| ISSN: | 1085-3375 1687-0409 |