Further Results of Mean-Value Type in \({\mathbb {C}}\) and \({\mathbb {R}}\)

  • Lubomir Markov
Part of the Studies in Computational Intelligence book series (SCI, volume 681)


We prove an extension of Pompeiu’s Mean Value Theorem to holomorphic functions in the spirit of the Evard-Jafari Theorem, a (new?) mean value theorem in \(\mathbb R,\) and an extension of the latter in \({\mathbb {C}}.\)


Evard-Jafari Theorem Complex Mean Value Theorem Flett’s Theorem Pompeiu’s Mean Value Theorem Davitt-Powers-Riedel-Sahoo Theorem 

2010 Mathematics Subject Classification:

30C15 26A24 30C99 


  1. 1.
    Davitt, R., Powers, R., Riedel, T., Sahoo, P.: Flett’s mean value theorem for holomorphic functions. Math. Mag. 72, 304–307 (1999)Google Scholar
  2. 2.
    Evard, J.-C., Jafari, F.: A complex Rolle’s Theorem. Amer. Math. Monthly 99, 858–861 (1992)Google Scholar
  3. 3.
    Flett, T.M.: A mean value theorem. Math. Gazette 42, 38–39 (1958)Google Scholar
  4. 4.
    Markov, L.: Mean value theorems for analytic functions. Serdica Math. J. 41, 471–480 (2015)MathSciNetGoogle Scholar
  5. 5.
    Pompeiu, D.: Sur une proposition analogue au théorème des accroissements finis. Mathematica (Cluj) 22, 143–146 (1946)Google Scholar
  6. 6.
    Sahoo, P., Riedel, T.: Mean Value Theorems and Functional Equations. World Scientific Publishing Singapore (1998)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and CSBarry UniversityMiami ShoresUSA

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