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

Yang-Hi Lee and Soon-Mo Jung
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Yang-Hi Lee: Department of Mathematics Education, Gongju National University of Education, Gongju 32553, Korea
Soon-Mo Jung: Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Korea

Mathematics, 2018, vol. 6, issue 12, 1-24

Abstract: 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.

Keywords: generalized Hyers–Ulam stability; functional equation; n -dimensional quartic-cubic-quadratic-additive type functional equation; direct method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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