Abstract
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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