Haruki, S.; Ng, C. T. Partial difference equations analogous to the Cauchy-Riemann equations and related functional equations on rings and fields. (English) Zbl 0830.39015 Result. Math. 26, No. 3-4, 316-323 (1994). Let \(S\) be a set endowed with two binary operations \((*)\) and \((\cdot)\) and \(G(+)\) be an Abelian group. The authors solve the functional equation \(f(x*t,y) + g(x,y \cdot t) = h(x,y)\), for \(x,y,t \in S\), where \(f,g,h : S \times S \to G\). Reviewer: Pl.Kannappan (Waterloo/Ontario) Cited in 1 Document MSC: 39B52 Functional equations for functions with more general domains and/or ranges 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable Keywords:partial difference equations; Cauchy-Riemann equations; Abelian group; functional equation PDFBibTeX XMLCite \textit{S. Haruki} and \textit{C. T. Ng}, Result. Math. 26, No. 3--4, 316--323 (1994; Zbl 0830.39015) Full Text: DOI References: [1] J. Aczél and S. Haruki, Partial difference equations analogous to the Cauchy-Riemann equations, Funkcial. Ekvac. 24(1981), 95–102. · Zbl 0487.39004 [2] W. Benz, Remark P191R1. (Contribution to T. M. Davison’s question), Aequationes Math. 20(1980), 307. [3] T. M. K. Davison, Problem (P191), Aequationes Math. 20(1980), 306. · doi:10.1007/BF02190522 [4] B. R. Ebanks, PL, Kannappan, and P. K. Sahoo, Cauchy differences that depend on the product of arguments, Glas. Mat. Ser. III 27(47)(1992), 251–261. · Zbl 0780.39007 [5] S. Haruki, Partial difference equations analogous to the Cauchy-Riemann equations, II, Funkcial. Ekvac. 29(1986), 237–241. · Zbl 0609.39007 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.