Generalized forms of Swiatak's functional equations with involution
Bull. Korean Math. Soc.
Published online 2019 Mar 13
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.
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