| Title:
|
Approximate tri-quadratic functional equations via Lipschitz conditions (English) |
| Author:
|
Nikoufar, Ismail |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
142 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
337-344 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we consider Lipschitz conditions for tri-quadratic functional equations. We introduce a new notion similar to that of the left invariant mean and prove that a family of functions with this property can be approximated by tri-quadratic functions via a Lipschitz norm. (English) |
| Keyword:
|
tri-quadratic functional equation |
| Keyword:
|
Lipschitz space |
| Keyword:
|
stability |
| MSC:
|
39B52 |
| MSC:
|
39B82 |
| idZBL:
|
Zbl 06819589 |
| idMR:
|
MR3739021 |
| DOI:
|
10.21136/MB.2017.0028-16 |
| . |
| Date available:
|
2017-11-20T15:00:38Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146973 |
| . |
| Reference:
|
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| Reference:
|
[2] Ebadian, A., Ghobadipour, N., Nikoufar, I., Gordji, M. Eshaghi: Approximation of the cubic functional equations in Lipschitz spaces.Anal. Theory Appl. 30 (2014), 354-362. Zbl 1340.39040, MR 3303361, 10.4208/ata.2014.v30.n4.2 |
| Reference:
|
[3] Jung, S.-M., Sahoo, P. K.: Hyers-Ulam stability of the quadratic equation of Pexider type.J. Korean Math. Soc. 38 (2001), 645-656. Zbl 0980.39023, MR 1826928 |
| Reference:
|
[4] Lee, J. R., Jang, S.-Y., Park, C., Shin, D. Y.: Fuzzy stability of quadratic functional equations.Adv. Difference Equ. 2010 (2010), Article ID 412160, 16 pages. Zbl 1192.39021, MR 2652450, 10.1155/2010/412160 |
| Reference:
|
[5] Nikoufar, I.: Lipschitz approximation of the $n$-quadratic functional equations.Mathematica (Cluj) - Tome 57 (2015), 67-74. MR 3611703 |
| Reference:
|
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| Reference:
|
[7] Nikoufar, I.: Erratum to: Quartic functional equations in Lipschitz spaces.Rend. Circ. Mat. Palermo, Ser. 2 65 (2016), 345-350. Zbl 06643403, MR 3535460, 10.1007/s12215-015-0222-x |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| . |
