A new version of the classical Rolle’s theorem is proved for any complex-valued differentiable function of the complex variable on an open connected convex subset of the complex field. The associated Mean-Value theorem follows naturally. A few explicit illustrative examples are provided in the closing section of the paper.
Pemba, J. P.; Davies, A. R.; and Muoneke, N. K.
A Complexification of Rolle’s Theorem,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 2,
1, Article 3.
Available at: https://digitalcommons.pvamu.edu/aam/vol2/iss1/3