Grząślewicz, Andrzej The general solution of the generalized Schilling’s equation. (English) Zbl 0765.39004 Aequationes Math. 44, No. 2-3, 317-326 (1992). The author extends a result which he presented at the 1991 Koninki (Poland) International Conference on Functional Equations and Inequalities (ICFEI). As generalization of “Schilling’s functional equation”, which arose from Physics, he offers the general solution of the equation \(Af(qx)=B(f(x+1)+Cf(x-1)+Df(x)\) \((x\in\mathbb{R})\), where \(A,D\in\mathbb{R}\), \(B,C\in\mathbb{R}\backslash\{0\}\), \(q\in[0,1]\) are otherwise arbitrary constants, and notes that it is determined by its values on [0,1]. Reviewer: J.Aczél (Waterloo / Ontario) MSC: 39B12 Iteration theory, iterative and composite equations 39B22 Functional equations for real functions Keywords:functional equation in a single variable; restriction; induction; equivalent conditions; Schilling’s functional equation PDFBibTeX XMLCite \textit{A. Grząślewicz}, Aequationes Math. 44, No. 2--3, 317--326 (1992; Zbl 0765.39004) Full Text: DOI EuDML References: [1] Baron, K. On a problem of R. Schilling. [Ber. Math.-Statist. Sekt. Forschungsgesellsch. Joanneum, Nr. 286]. J. Forschungszentrum, Graz, 1988. 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.