Lee, Y.-H.; Jung, S.-M. A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations. Mathematics2018, 6, 282.
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.
Lee, Y.-H.; Jung, S.-M. A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations. Mathematics2018, 6, 282.
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.
Abstract
We prove general stability theorems for $n$-dimensional quartic-cubic-quadratic-additive type functional equations of the form \begin{eqnarray*} \sum_{i=1}^\ell c_i f \big( a_{i1}x_1 + a_{i2}x_2 + \cdots + a_{in}x_n \big) = 0 \end{eqnarray*} by applying the direct method. These stability theorems can save us much 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
Subject
Computer Science and Mathematics, Analysis
Copyright:
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