aequationes mathematicae

, Volume 44, Issue 2–3, pp 317–326 | Cite as

The general solution of the generalized Schilling's equation

  • Andrzej Grzaślewicz
Research Papers
  • 18 Downloads

Summary

In this note it is shown that the solutionf: ℝ → ℝ of the functional equation
$$Af(qx) = Bf(x + 1) + Cf(x - 1) + Df(x) for x \in \mathbb{R}$$
(1)
(A, D ∈ ℝ, B, C ∈ ℝ − {0}, q ∈ [0, 1] are arbitrary constants) is uniquely defined by the restrictionf[−1,1] satisfying the following condition
$$(A - D)f(0) = Bf(1) + Cf( - 1).$$
Moreover, the general solution of equation (1) is presented.

AMS (1991) subject classification

39A20 

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Reference

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

Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • Andrzej Grzaślewicz
    • 1
  1. 1.Instytut MatematykiWyŻsza Szkola PedagogicznaKrakowPoland

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