Gselmann, Eszter and Małolepszy, Tomasz and Matkowski, Janusz (2026) Perturbations of Cauchy differences. AEQUATIONES MATHEMATICAE, 100. ISSN 0001-9054 (print); 1420-8903 (online)
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Abstract
Our results extend previous work on the bilinearity of the Cauchy exponential difference by Alzer and Matkowski. We characterize solutions under various structural and regularity assumptions, including additive and exponential Cauchy differences, and show that solutions often reduce to additive functions, exponential polynomials, or combinations thereof. For Levi-Civita type equations, we provide explicit representations of solutions in terms of additive and exponential components. Furthermore, we determine conditions under which real-valued solutions exist and describe their forms. The paper concludes with open problems concerning generalized equations that cannot be solved by the methods presented here, suggesting directions for future research.
| Item Type: | Article |
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| Uncontrolled Keywords: | Cauchy difference, functional equations, biadditive perturbations, additive and multiplicative functions, exponential polynomials, Levi-Civita equations |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis |
| Depositing User: | Dr. Novák-Gselmann Eszter |
| Date Deposited: | 02 Sep 2026 09:56 |
| Last Modified: | 02 Sep 2026 09:56 |
| URI: | https://real.mtak.hu/id/eprint/245152 |
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