Generalized forms of Swiatak's functional equations with involution
Bull. Korean Math. Soc. 2019 Vol. 56, No. 3, 779-787
Published online March 13, 2019
Printed May 31, 2019
Zhihua Wang
Hubei University of Technology
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
MSC numbers : 39B82, 39B52
Supported by : The author is supported by the National Natural Science Foundation of China (Grant Nos. 11401190) and 17YJA790098
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