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Article

A Uniqueness Theorem for Stability Problems of Functional Equations

1
Nano Convergence Technology Research Institute, School of Semiconductor · Display Technology, Hallym University, Chuncheon 24252, Republic of Korea
2
Department of Mathematics Education, Gongju National University of Education, Gongju 32553, Republic of Korea
3
Ilsong Liberal Art Schools (Mathematics), Hallym University, Chuncheon 24252, Republic of Korea
*
Author to whom correspondence should be addressed.
Symmetry 2024, 16(10), 1298; https://doi.org/10.3390/sym16101298
Submission received: 16 July 2024 / Revised: 9 September 2024 / Accepted: 18 September 2024 / Published: 2 October 2024

Abstract

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.
Keywords: uniqueness; stability; generalized stability; monomial mapping; generalized polynomial mapping of degree n uniqueness; stability; generalized stability; monomial mapping; generalized polynomial mapping of degree n

Share and Cite

MDPI and ACS Style

Jung, S.-M.; Lee, Y.-H.; Roh, J. A Uniqueness Theorem for Stability Problems of Functional Equations. Symmetry 2024, 16, 1298. https://doi.org/10.3390/sym16101298

AMA Style

Jung S-M, Lee Y-H, Roh J. A Uniqueness Theorem for Stability Problems of Functional Equations. Symmetry. 2024; 16(10):1298. https://doi.org/10.3390/sym16101298

Chicago/Turabian Style

Jung, Soon-Mo, Yang-Hi Lee, and Jaiok Roh. 2024. "A Uniqueness Theorem for Stability Problems of Functional Equations" Symmetry 16, no. 10: 1298. https://doi.org/10.3390/sym16101298

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