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On an application of hypoellipticity to solutions of functional equations

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Summary

We study the regularity of solutions of functional equations of a generalized mean value type. In this paper we give sufficient conditions for the regularity by using hypoellipticity which is a concept of the theory of partial differential equations. We also give an affirmative answer to a conjecture of H. Światak. A part of the results was announced in the comprehensive paper [8] on our joint works. To prove the regularity of solutions of functional equations is one of the central problems in the theory of functional equations (see [1]).

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Authors and Affiliations

  1. Department of Applied Mathematics, Osaka Women's University, 590, Sakai, Osaka, Japan

    Akira Tsutsumi & Shigeru Haruki

  2. Department of Applied Mathematics, Graduate School, Okayama University of Science, 700, Ridai-cho, Okayama, Japan

    Akira Tsutsumi & Shigeru Haruki

Authors
  1. Akira Tsutsumi
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  2. Shigeru Haruki
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Tsutsumi, A., Haruki, S. On an application of hypoellipticity to solutions of functional equations. Aeq. Math. 51, 270–276 (1996). https://doi.org/10.1007/BF01833282

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  • DOI: https://doi.org/10.1007/BF01833282

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