Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 34, pp. 1-6.
Title: Mean value theorem for holomorphic functions
Authors: Devrim Cakmak (Gazi Univ., Ankara, Turkey)
Aydin Tiryaki (Izmir Univ., Izmir, Turkey)
Abstract:
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.