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http://dx.doi.org/10.4134/BKMS.b180594

GENERALIZED FORMS OF SWIATAK'S FUNCTIONAL EQUATIONS WITH INVOLUTION  

Wang, Zhihua (School of Science Hubei University of Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.56, no.3, 2019 , pp. 779-787 More about this Journal
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;
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