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A method of solving functional equations on convex subsets of linear spaces

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Summary.

We introduce a method of solving a wide range of functional equations stemming from Mean Value Theorems. We generalize the results of Z. Daróczy and Gy. Maksa (Corollary 2; [2]) in the spirit of M. Sablik’s lemma (Lemma 2.3; [11]). Next, we illustrate the method taking into account two functional equations. The first one is connected with Flett’s Mean Value Theorem ([6]) and the second one is derived from Simpson’s rule ([10]).

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Authors and Affiliations

  1. Institute of Mathematics, Silesian University, ul. Bankowa 14, Pl-40-007, Katowice, Poland

    Iwona Pawlikowska

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  1. Iwona Pawlikowska
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Correspondence to Iwona Pawlikowska.

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Manuscript received: August 9, 2004 and, in final form, June 29, 2006.

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Pawlikowska, I. A method of solving functional equations on convex subsets of linear spaces. Aequ. math. 75, 1–28 (2008). https://doi.org/10.1007/s00010-007-2881-y

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  • DOI: https://doi.org/10.1007/s00010-007-2881-y

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