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

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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