On Pexider Differences in Topological Vector Spaces
Let 𝑋 be a normed space and 𝑌 a sequentially complete Hausdorff topological vector space over the field ℚ of rational numbers. Let 𝐷1={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖≥𝑑}, and 𝐷2={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖<𝑑} where 𝑑>0. We prove that the Pexiderized Jensen functional equation is stable for functions defined on 𝐷1(𝐷2...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/370104 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Let 𝑋 be a normed space and 𝑌 a sequentially complete Hausdorff topological vector space over the field ℚ of rational numbers. Let 𝐷1={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖≥𝑑}, and 𝐷2={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖<𝑑} where 𝑑>0. We prove that the Pexiderized Jensen functional equation is stable for functions defined on 𝐷1(𝐷2), and taking values in 𝑌. We consider also the Pexiderized Cauchy functional equation. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |