Paper Title:

The Functional Equation With an Exponential Polynomial Solution and its Stability

Author(s):

Young Whan Lee¹, Gwang Hui Kim^2*, and Jeong Il Kim³

¹Department of Computer Hacking and Information Security,
College of Engineering, Daejeon University,
Daejeon, 34520,
Korea(Republic of).
E-mail: ywlee@dju.ac.kr

²Department of Mathematics,
Kangnam University,
Yongin, Gyeonggi, 16979,
Korea(Republic of).
E-mail: ighkim@kangnam.ac.kr

³Department of Statistics,
Daejeon University,
Daejeon 34520,
Korea(Republic of).
E-mail: jlkim@dju.ac.kr

Abstract:

In this paper, we prove that the unique continuous solution of the functional equation

is

where p_n(x) is a polynomial with degree n and

We also obtain the superstability and stability of the functional equation with the following forms, respectively:

and

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