The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

The Functional Equation With an Exponential Polynomial Solution and its Stability


Young Whan Lee1, Gwang Hui Kim2*, and Jeong Il Kim3

1Department of Computer Hacking and Information Security,
College of Engineering, Daejeon University,
Daejeon, 34520,
Korea(Republic of).

2Department of Mathematics,
Kangnam University,
Yongin, Gyeonggi, 16979,
Korea(Republic of).
E-mail: i

3Department of Statistics,
Daejeon University,
Daejeon 34520,
Korea(Republic of).


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


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

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



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