Geodesic
Mean value theorem for holomorphic functions
Electronic journal of differential equations, Tome 2012 (2012)
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.
Classification : 39B22, 26A24
Keywords: rolle's theorem, mean value theorem, flett's theorem, holomorphic function 
@article{EJDE_2012__2012__a73,
     author = {\c{C}akmak,  Devrim and Tiryaki,  Aydin},
     title = {Mean value theorem for holomorphic functions},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1248.30002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a73/}
}
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AU  - Tiryaki,  Aydin
TI  - Mean value theorem for holomorphic functions
JO  - Electronic journal of differential equations
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VL  - 2012
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%A Tiryaki,  Aydin
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%J Electronic journal of differential equations
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%F EJDE_2012__2012__a73
Çakmak,  Devrim; Tiryaki,  Aydin. Mean value theorem for holomorphic functions. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a73/