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A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations

by Yang-Hi Lee 1 and Soon-Mo Jung 2,*
1
Department of Mathematics Education, Gongju National University of Education, Gongju 32553, Korea
2
Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 282; https://doi.org/10.3390/math6120282
Received: 21 October 2018 / Revised: 13 November 2018 / Accepted: 21 November 2018 / Published: 26 November 2018
We prove general stability theorems for n-dimensional quartic-cubic-quadratic-additive type functional equations of the form i = 1 c i f a i 1 x 1 + a i 2 x 2 + + a i n x n = 0 . by applying the direct method. These stability theorems can save us the trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations. View Full-Text
Keywords: generalized Hyers–Ulam stability; functional equation; n-dimensional quartic-cubic-quadratic-additive type functional equation; direct method generalized Hyers–Ulam stability; functional equation; n-dimensional quartic-cubic-quadratic-additive type functional equation; direct method
MDPI and ACS Style

Lee, Y.-H.; Jung, S.-M. A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations. Mathematics 2018, 6, 282.

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