### Journals Information

**
Mathematics and Statistics Vol. 8(3), pp. 363 - 371 DOI: 10.13189/ms.2020.080316 Reprint (PDF) (259Kb) **

## Superstability and Solution of The Pexiderized Trigonometric Functional Equation

**Gwang Hui Kim ^{*}**

Department of Mathematics, Kangnam University Yongin, Gyeonggi, 16979, Korea

**ABSTRACT**

The present work continues the study for the superstability and solution of the Pexider type functional equation , which is the mixed functional equation represented by sum of the sine, cosine, tangent, hyperbolic trigonometric, and exponential functions. The stability of the cosine (d'Alembert) functional equation and the Wilson equation was researched by many authors: Baker [7], Badora [5], Kannappan [14], Kim ([16, 19]), and Fassi, etc [11]. The stability of the sine type equations was researched by Cholewa [10], Kim ([18], [20]). The stability of the difference type equation for the above equation was studied by Kim ([21], [22]). In this paper, we investigate the superstability of the sine functional equation and the Wilson equation from the Pexider type difference functional equation , which is the mixed equation represented by the sine, cosine, tangent, hyperbolic trigonometric functions, and exponential functions. Also, we obtain additionally that the Wilson equation and the cosine functional eqaution in the obtained results can be represented by the composition of a homomorphism. In here, the domain (G; +) of functions is a noncommutative semigroup (or 2-divisible Abelian group), and A is an unital commutative normed algebra with unit 1A. The obtained results can be applied and expanded to the stability for the difference type's functional equation which consists of the (hyperbolic) secant, cosecant, logarithmic functions.

**KEYWORDS**

Stability, Superstability, Cosine Functional Equation, Sine Functional Equation, Trigonometric Functional Equation

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

(a). IEEE Format:

[1] Gwang Hui Kim , "Superstability and Solution of The Pexiderized Trigonometric Functional Equation," Mathematics and Statistics, Vol. 8, No. 3, pp. 363 - 371, 2020. DOI: 10.13189/ms.2020.080316.

(b). APA Format:

Gwang Hui Kim (2020). Superstability and Solution of The Pexiderized Trigonometric Functional Equation. Mathematics and Statistics, 8(3), 363 - 371. DOI: 10.13189/ms.2020.080316.