On new stability results for composite functional equations in quasi-β-normed spaces
In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f(f(x)−f(y))=f(x+y)+f(x−y)−f(x)−f(y),f(f\left(x)-f(y))=f\left(x+y)+f\left(x-y)-f\left(x)-f(y), where ff maps from a (β,p)\left(\beta ,p)-Banach space into itself, by using the fixe...
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De Gruyter
2021
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oai:doaj.org-article:2d89295e5ab343e780ee60d62981373a2021-12-05T14:10:45ZOn new stability results for composite functional equations in quasi-β-normed spaces2391-466110.1515/dema-2021-0002https://doaj.org/article/2d89295e5ab343e780ee60d62981373a2021-04-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0002https://doaj.org/toc/2391-4661In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f(f(x)−f(y))=f(x+y)+f(x−y)−f(x)−f(y),f(f\left(x)-f(y))=f\left(x+y)+f\left(x-y)-f\left(x)-f(y), where ff maps from a (β,p)\left(\beta ,p)-Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite ss-functional inequality is discussed via our results.Thanyacharoen AnurakSintunavarat WutipholDe Gruyterarticleadditive functional equationscomposite functional equationscomposite s-functional inequalitiesquasi-β-normed spaces39b3230d0547h1046h25MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 68-84 (2021) |
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DOAJ |
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DOAJ |
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EN |
| topic |
additive functional equations composite functional equations composite s-functional inequalities quasi-β-normed spaces 39b32 30d05 47h10 46h25 Mathematics QA1-939 |
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additive functional equations composite functional equations composite s-functional inequalities quasi-β-normed spaces 39b32 30d05 47h10 46h25 Mathematics QA1-939 Thanyacharoen Anurak Sintunavarat Wutiphol On new stability results for composite functional equations in quasi-β-normed spaces |
| description |
In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f(f(x)−f(y))=f(x+y)+f(x−y)−f(x)−f(y),f(f\left(x)-f(y))=f\left(x+y)+f\left(x-y)-f\left(x)-f(y), where ff maps from a (β,p)\left(\beta ,p)-Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite ss-functional inequality is discussed via our results. |
| format |
article |
| author |
Thanyacharoen Anurak Sintunavarat Wutiphol |
| author_facet |
Thanyacharoen Anurak Sintunavarat Wutiphol |
| author_sort |
Thanyacharoen Anurak |
| title |
On new stability results for composite functional equations in quasi-β-normed spaces |
| title_short |
On new stability results for composite functional equations in quasi-β-normed spaces |
| title_full |
On new stability results for composite functional equations in quasi-β-normed spaces |
| title_fullStr |
On new stability results for composite functional equations in quasi-β-normed spaces |
| title_full_unstemmed |
On new stability results for composite functional equations in quasi-β-normed spaces |
| title_sort |
on new stability results for composite functional equations in quasi-β-normed spaces |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/2d89295e5ab343e780ee60d62981373a |
| work_keys_str_mv |
AT thanyacharoenanurak onnewstabilityresultsforcompositefunctionalequationsinquasibnormedspaces AT sintunavaratwutiphol onnewstabilityresultsforcompositefunctionalequationsinquasibnormedspaces |
| _version_ |
1718371759689826304 |