Electron. J. Diff. Equ., Vol. 2012 (2012), No. 34, pp. 1-6.

Mean value theorem for holomorphic functions

Devrim Cakmak, Aydin Tiryaki

This article presents a generalization of Myers' theorem and when the boundary assumption f'(a)=f'(b) is removed, and to prove this result for holomorphic functions of one complex variable. After that, the equivalence of Rolle's and mean value theorems in the complex plane are proved.

Submitted November 29, 2011. Published February 29, 2012.
Math Subject Classifications: 39B22, 26A24.
Key Words: Rolle's theorem; mean value theorem; Flett's theorem; holomorphic function.

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Devrim Çakmak
Gazi University, Faculty of Education
Department of Mathematics Education
06500 Teknikokullar - Ankara, Turkey
email: dcakmak@gazi.edu.tr
Aydin Tiryaki
Izmir University, Faculty of Arts and Sciences
Department of Mathematics and Computer Sciences
35350 Uckuyular - Izmir, Turkey
email: aydin.tiryaki@izmir.edu.tr

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