Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2019; 56(3): 779-787

Online first article March 13, 2019      Printed May 31, 2019

https://doi.org/10.4134/BKMS.b180594

Copyright © The Korean Mathematical Society.

Generalized forms of Swiatak's functional equations with involution

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