aequationes mathematicae

, Volume 60, Issue 3, pp 258–267 | Cite as

Taylor's theorem and functional equations

  • M. Sablik


Several authors (cf. [1]—[10]) studied functional equations stemming from Mean Value Theorems. In the present paper we solve an equation that originates from Taylor's formula, viz.¶¶\( f(y) = \sum\limits_{k=0}^{n-2} \gamma_k(x)(y-x)^k + \phi (( 1-\frac{1}{n}) x + \frac{1}{n}y)(y-x)^{n-1} \).¶No regularity assumptions are assumed and all the functions are unknown, defined and taking values in Abelian groups.

Keywords. Functional equations, polynomial functions, Taylor's theorem. 


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Copyright information

© Birkhäuser Verlag, Basel, 2000

Authors and Affiliations

  • M. Sablik
    • 1
  1. 1. Institute of Mathematics, Silesian University, Bankowa 14, PL—40 007 Katowice, PolandPL

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