On a General Conditional Cauchy Functional Equation
Let $(G,+)$ be an abelian group and $Y$ a linear space over the field $\Bbb{F}\in\{\Bbb{R}, \Bbb{C}\}$. In this paper, we investigate the conditional Cauchy functional equation \[f(x+y)\neq af(x)+bf(y)\quad\Rightarrow \quad f(x+y)=f(x)+f(y),\quad x,y\in G,\] for functions $f:G\to Y$, where $a,b\in...
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University of Maragheh
2024-03-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_710730_1097db7f4cdaf2bb076df721ce97d691.pdf |
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| _version_ | 1823859383239442432 |
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| author | Elham Mohammadi Abbas Najati Yavar Khedmati Yengejeh |
| author_facet | Elham Mohammadi Abbas Najati Yavar Khedmati Yengejeh |
| author_sort | Elham Mohammadi |
| collection | DOAJ |
| description | Let $(G,+)$ be an abelian group and $Y$ a linear space over the field $\Bbb{F}\in\{\Bbb{R}, \Bbb{C}\}$. In this paper, we investigate the conditional Cauchy functional equation \[f(x+y)\neq af(x)+bf(y)\quad\Rightarrow \quad f(x+y)=f(x)+f(y),\quad x,y\in G,\] for functions $f:G\to Y$, where $a,b\in \Bbb{F}$ are fixed constants. The general solution and stability of this functional equation are described. |
| format | Article |
| id | doaj-art-2a3665ad9b59459686f8902977c24207 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-2a3665ad9b59459686f8902977c242072025-02-11T05:24:46ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-03-0121231532610.22130/scma.2023.2006802.1386710730On a General Conditional Cauchy Functional EquationElham Mohammadi0Abbas Najati1Yavar Khedmati Yengejeh2Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.Let $(G,+)$ be an abelian group and $Y$ a linear space over the field $\Bbb{F}\in\{\Bbb{R}, \Bbb{C}\}$. In this paper, we investigate the conditional Cauchy functional equation \[f(x+y)\neq af(x)+bf(y)\quad\Rightarrow \quad f(x+y)=f(x)+f(y),\quad x,y\in G,\] for functions $f:G\to Y$, where $a,b\in \Bbb{F}$ are fixed constants. The general solution and stability of this functional equation are described.https://scma.maragheh.ac.ir/article_710730_1097db7f4cdaf2bb076df721ce97d691.pdfabelian groupconditional functional equationmikusiński’s functional equationstability |
| spellingShingle | Elham Mohammadi Abbas Najati Yavar Khedmati Yengejeh On a General Conditional Cauchy Functional Equation Sahand Communications in Mathematical Analysis abelian group conditional functional equation mikusiński’s functional equation stability |
| title | On a General Conditional Cauchy Functional Equation |
| title_full | On a General Conditional Cauchy Functional Equation |
| title_fullStr | On a General Conditional Cauchy Functional Equation |
| title_full_unstemmed | On a General Conditional Cauchy Functional Equation |
| title_short | On a General Conditional Cauchy Functional Equation |
| title_sort | on a general conditional cauchy functional equation |
| topic | abelian group conditional functional equation mikusiński’s functional equation stability |
| url | https://scma.maragheh.ac.ir/article_710730_1097db7f4cdaf2bb076df721ce97d691.pdf |
| work_keys_str_mv | AT elhammohammadi onageneralconditionalcauchyfunctionalequation AT abbasnajati onageneralconditionalcauchyfunctionalequation AT yavarkhedmatiyengejeh onageneralconditionalcauchyfunctionalequation |