# GENERALIZED FORMS OF SWIATAK'S FUNCTIONAL EQUATIONS WITH INVOLUTION

• Wang, Zhihua (School of Science Hubei University of Technology)
• Received : 2018.06.22
• Accepted : 2019.01.08
• Published : 2019.05.31
• 63 8

#### Abstract

In this paper, we study two functional equations with two unknown functions from an Abelian group into a commutative ring without zero divisors. The two equations are generalizations of Swiatak's functional equations with an involution. We determine the general solutions of the two functional equations and the properties of the general solutions of the two functional equations under three different hypotheses, respectively. For one of the functional equations, we establish the Hyers-Ulam stability in the case that the unknown functions are complex valued.

#### Keywords

abelian group;Hyers-Ulam stability;quadratic functional equation;Swiatak's functional equation

#### Acknowledgement

Supported by : National Natural Science Foundation of China

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