A Remark for the Hyers–Ulam Stabilities on <i>n</i>-Banach Spaces
In this article, we deal with stabilities of several functional equations in <i>n</i>-Banach spaces. For a surjective mapping <i>f</i> into a <i>n</i>-Banach space, we prove the generalized Hyers–Ulam stabilities of the cubic functional equation and the quartic fu...
| Published in: | Axioms |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-12-01
|
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/10/1/2 |
| _version_ | 1850424808577171456 |
|---|---|
| author | Jaeyoo Choy Hahng-Yun Chu Ahyoung Kim |
| author_facet | Jaeyoo Choy Hahng-Yun Chu Ahyoung Kim |
| author_sort | Jaeyoo Choy |
| collection | DOAJ |
| container_title | Axioms |
| description | In this article, we deal with stabilities of several functional equations in <i>n</i>-Banach spaces. For a surjective mapping <i>f</i> into a <i>n</i>-Banach space, we prove the generalized Hyers–Ulam stabilities of the cubic functional equation and the quartic functional equation for <i>f</i> in <i>n</i>-Banach spaces. |
| format | Article |
| id | doaj-art-e9e9cbdcdff240f9898bac42db26eee1 |
| institution | Directory of Open Access Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| spelling | doaj-art-e9e9cbdcdff240f9898bac42db26eee12025-08-19T22:41:10ZengMDPI AGAxioms2075-16802020-12-01101210.3390/axioms10010002A Remark for the Hyers–Ulam Stabilities on <i>n</i>-Banach SpacesJaeyoo Choy0Hahng-Yun Chu1Ahyoung Kim2School of Mathematics, KIAS, 85 Hoegi-ro, Dongdaemun-Gu, Seoul 02455, KoreaDepartment of Mathematics, Chungnam National University, 79 Daehak-ro, Yuseong-Gu, Daejeon 34134, KoreaDepartment of Mathematics, Chungnam National University, 79 Daehak-ro, Yuseong-Gu, Daejeon 34134, KoreaIn this article, we deal with stabilities of several functional equations in <i>n</i>-Banach spaces. For a surjective mapping <i>f</i> into a <i>n</i>-Banach space, we prove the generalized Hyers–Ulam stabilities of the cubic functional equation and the quartic functional equation for <i>f</i> in <i>n</i>-Banach spaces.https://www.mdpi.com/2075-1680/10/1/2<i>n</i>-Banach spacecubic mappingsquartic mappingsthe generalized Hyers–Ulam stability |
| spellingShingle | Jaeyoo Choy Hahng-Yun Chu Ahyoung Kim A Remark for the Hyers–Ulam Stabilities on <i>n</i>-Banach Spaces <i>n</i>-Banach space cubic mappings quartic mappings the generalized Hyers–Ulam stability |
| title | A Remark for the Hyers–Ulam Stabilities on <i>n</i>-Banach Spaces |
| title_full | A Remark for the Hyers–Ulam Stabilities on <i>n</i>-Banach Spaces |
| title_fullStr | A Remark for the Hyers–Ulam Stabilities on <i>n</i>-Banach Spaces |
| title_full_unstemmed | A Remark for the Hyers–Ulam Stabilities on <i>n</i>-Banach Spaces |
| title_short | A Remark for the Hyers–Ulam Stabilities on <i>n</i>-Banach Spaces |
| title_sort | remark for the hyers ulam stabilities on i n i banach spaces |
| topic | <i>n</i>-Banach space cubic mappings quartic mappings the generalized Hyers–Ulam stability |
| url | https://www.mdpi.com/2075-1680/10/1/2 |
| work_keys_str_mv | AT jaeyoochoy aremarkforthehyersulamstabilitiesoninibanachspaces AT hahngyunchu aremarkforthehyersulamstabilitiesoninibanachspaces AT ahyoungkim aremarkforthehyersulamstabilitiesoninibanachspaces AT jaeyoochoy remarkforthehyersulamstabilitiesoninibanachspaces AT hahngyunchu remarkforthehyersulamstabilitiesoninibanachspaces AT ahyoungkim remarkforthehyersulamstabilitiesoninibanachspaces |