{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T02:42:50Z","timestamp":1772592170644,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,2]],"date-time":"2024-10-02T00:00:00Z","timestamp":1727827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of Korea (NRF)","award":["2021R1A2C109489611"],"award-info":[{"award-number":["2021R1A2C109489611"]}]},{"name":"Korea government (MSIT)","award":["2021R1A2C109489611"],"award-info":[{"award-number":["2021R1A2C109489611"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we present a uniqueness theorem obtained by using direct calculation. This theorem is applicable to stability problems of functional equations whose solutions are monomial or generalized polynomial mappings of degree n. The advantage of this uniqueness theorem is that it simplifies the proof by eliminating the need to repeatedly and cumbersomely prove uniqueness in stability studies.<\/jats:p>","DOI":"10.3390\/sym16101298","type":"journal-article","created":{"date-parts":[[2024,10,2]],"date-time":"2024-10-02T06:27:31Z","timestamp":1727850451000},"page":"1298","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Uniqueness Theorem for Stability Problems of Functional Equations"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6812-016X","authenticated-orcid":false,"given":"Soon-Mo","family":"Jung","sequence":"first","affiliation":[{"name":"Nano Convergence Technology Research Institute, School of Semiconductor \u00b7 Display Technology, Hallym University, Chuncheon 24252, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang-Hi","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Gongju National University of Education, Gongju 32553, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaiok","family":"Roh","sequence":"additional","affiliation":[{"name":"Ilsong Liberal Art Schools (Mathematics), Hallym University, Chuncheon 24252, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1090\/S0002-9939-05-07841-X","article-title":"A general functional equation and its stability","volume":"133","author":"Baker","year":"2005","journal-title":"Proc. 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