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The general solution of the generalized Schilling’s equation. (English) Zbl 0765.39004

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].

MSC:

39B12 Iteration theory, iterative and composite equations
39B22 Functional equations for real functions
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References:

[1] Baron, K. On a problem of R. Schilling. [Ber. Math.-Statist. Sekt. Forschungsgesellsch. Joanneum, Nr. 286]. J. Forschungszentrum, Graz, 1988.
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