### Journals Information

**
Mathematics and Statistics Vol. 7(1), pp. 25 - 32 DOI: 10.13189/ms.2019.070104 Reprint (PDF) (261Kb) **

## Hyperstability and Stability of a Logarithm-type Functional Equation

**Young Whan Lee ^{1}, Gwang Hui Kim ^{2}^{,*}**

^{1}Department of Computer Hacking and Information Security, College of Engineering, Daejeon University, Daejeon, 34520, Korea

^{2}Department of Mathematics, Kangnam University, Yongin, Gyeonggi, 16979, Korea

**ABSTRACT**

In 2001, Maksa and P´ales [12] introduced a new type’s stability: hyperstability for a class of linear functional equation. Riedel and Sahoo [14] have generalized a functional equation associated with the distance between the probability distributions, which is . Elfen etc. [7] obtained the solution of the functional equation on semigroup G. The aim of this paper is to investigate the hyperstability and the Hyers-Ulam stability for the above Logarithm-type functional equation considered by Elfen, etc. Namely, if f is an approximative equation related to the above equation, then it is a solution of this equation which exists within " bound of a given approximative function f.

**KEYWORDS**

Information Measure, Distance Measure, Superstability, Multiplicative Function, Stability of Functional Equation

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Young Whan Lee , Gwang Hui Kim , "Hyperstability and Stability of a Logarithm-type Functional Equation," Mathematics and Statistics, Vol. 7, No. 1, pp. 25 - 32, 2019. DOI: 10.13189/ms.2019.070104.

(b). APA Format:

Young Whan Lee , Gwang Hui Kim (2019). Hyperstability and Stability of a Logarithm-type Functional Equation. Mathematics and Statistics, 7(1), 25 - 32. DOI: 10.13189/ms.2019.070104.