Hyperstability of Cauchy and Jensen functional equations in 2-normed spaces
Abstract In this article, with simple and short proofs without applying fixed point theorems, some hyperstability results corresponding to the functional equations of Cauchy and Jensen are presented in 2-normed spaces. We also obtain some results on hyperstability for the general linear functional e...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-04-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-024-03116-2 |
| _version_ | 1797219537091821568 |
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| author | Abbas Najati Yavar Khedmati Yengejeh Kandhasamy Tamilvanan Masho Jima Kabeto |
| author_facet | Abbas Najati Yavar Khedmati Yengejeh Kandhasamy Tamilvanan Masho Jima Kabeto |
| author_sort | Abbas Najati |
| collection | DOAJ |
| description | Abstract In this article, with simple and short proofs without applying fixed point theorems, some hyperstability results corresponding to the functional equations of Cauchy and Jensen are presented in 2-normed spaces. We also obtain some results on hyperstability for the general linear functional equation f ( a x + b y ) = A f ( x ) + B f ( y ) + C $f(ax+by)=Af(x)+Bf(y)+C$ . |
| first_indexed | 2024-04-24T12:35:13Z |
| format | Article |
| id | doaj.art-8841cc0cdbb44b9897dc652dc6a9002b |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-24T12:35:13Z |
| publishDate | 2024-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-8841cc0cdbb44b9897dc652dc6a9002b2024-04-07T11:34:01ZengSpringerOpenJournal of Inequalities and Applications1029-242X2024-04-012024111310.1186/s13660-024-03116-2Hyperstability of Cauchy and Jensen functional equations in 2-normed spacesAbbas Najati0Yavar Khedmati Yengejeh1Kandhasamy Tamilvanan2Masho Jima Kabeto3Department of Mathematics, University of Mohaghegh ArdabiliDepartment of Mathematics, University of Mohaghegh ArdabiliDepartment of Mathematics, Faculty of Science and Humanities, R. M. K. Engineering CollegeDepartment of Mathematics, College of Natural Sciences, Jimma UniversityAbstract In this article, with simple and short proofs without applying fixed point theorems, some hyperstability results corresponding to the functional equations of Cauchy and Jensen are presented in 2-normed spaces. We also obtain some results on hyperstability for the general linear functional equation f ( a x + b y ) = A f ( x ) + B f ( y ) + C $f(ax+by)=Af(x)+Bf(y)+C$ .https://doi.org/10.1186/s13660-024-03116-22-normed spaceCauchy functional equationJensen functional equationGeneral linear functional equationHyperstability |
| spellingShingle | Abbas Najati Yavar Khedmati Yengejeh Kandhasamy Tamilvanan Masho Jima Kabeto Hyperstability of Cauchy and Jensen functional equations in 2-normed spaces Journal of Inequalities and Applications 2-normed space Cauchy functional equation Jensen functional equation General linear functional equation Hyperstability |
| title | Hyperstability of Cauchy and Jensen functional equations in 2-normed spaces |
| title_full | Hyperstability of Cauchy and Jensen functional equations in 2-normed spaces |
| title_fullStr | Hyperstability of Cauchy and Jensen functional equations in 2-normed spaces |
| title_full_unstemmed | Hyperstability of Cauchy and Jensen functional equations in 2-normed spaces |
| title_short | Hyperstability of Cauchy and Jensen functional equations in 2-normed spaces |
| title_sort | hyperstability of cauchy and jensen functional equations in 2 normed spaces |
| topic | 2-normed space Cauchy functional equation Jensen functional equation General linear functional equation Hyperstability |
| url | https://doi.org/10.1186/s13660-024-03116-2 |
| work_keys_str_mv | AT abbasnajati hyperstabilityofcauchyandjensenfunctionalequationsin2normedspaces AT yavarkhedmatiyengejeh hyperstabilityofcauchyandjensenfunctionalequationsin2normedspaces AT kandhasamytamilvanan hyperstabilityofcauchyandjensenfunctionalequationsin2normedspaces AT mashojimakabeto hyperstabilityofcauchyandjensenfunctionalequationsin2normedspaces |