{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T05:54:02Z","timestamp":1772171642321,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T00:00:00Z","timestamp":1740009600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we deal with a general functional equation in several variables. We prove the hyperstability of this equation in (m + 1)-normed spaces and describe its general solution in some special cases. In this way, we solve the problems posed by Ciepli\u0144ski. The considered equation was introduced as a generalization of the equation characterizing n-quadratic functions and has symmetric coefficients (up to sign), and it also generalizes many other known functional equations with symmetric coefficients, such as the multi-Cauchy equation, the multi-Jensen equation, and the multi-Cauchy\u2013Jensen equation. Our results generalize several known results.<\/jats:p>","DOI":"10.3390\/sym17030320","type":"journal-article","created":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T11:03:37Z","timestamp":1740049417000},"page":"320","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On a General Functional Equation"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6041-3152","authenticated-orcid":false,"given":"Anna","family":"Bahyrycz","sequence":"first","affiliation":[{"name":"AGH University of Krakow, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krak\u00f3w, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,20]]},"reference":[{"key":"ref_1","unstructured":"Acz\u00e9l, J. (1966). Lectures on Functional Equations and Their Applications, Academic Press."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Acz\u00e9l, J., and Dhombres, J. (1989). Functional Equations in Several Variables. Encyclopedia of Mathematics and Its Applications, 31, Cambridge University Press.","DOI":"10.1017\/CBO9781139086578"},{"key":"ref_3","first-page":"209","article-title":"Generalized stability of multi-quadratic mappings","volume":"34","author":"Ji","year":"2014","journal-title":"J. Math. Res. Appl."},{"key":"ref_4","first-page":"1","article-title":"Ulam stability of functional equations in 2-Banach spaces via the fixed point method","volume":"23","year":"2021","journal-title":"J. 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Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/s00025-020-01275-4","article-title":"On Ulam stability of a functional equation","volume":"75","year":"2020","journal-title":"Results Math."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Jung, S.-M. (2011). Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer.","DOI":"10.1007\/978-1-4419-9637-4"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4134\/BKMS.2008.45.1.133","article-title":"Stability of the multi-Jensen equation","volume":"45","author":"Prager","year":"2008","journal-title":"Bull. Korean Math. Soc."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zhao, K., Liu, J., and Lv, X. (2024). A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm\u2013Liouville Equations with CH\u2013Fractional Derivatives and Impulses via Coincidence Theory. 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