complex mean-value theorem

Theorem [1] Suppose Ω is an open convex set in , suppose f is a holomorphic functionMathworldPlanetmath f:Ω, and suppose a,b are distinct points in Ω. Then there exist points u,v on Lab (the straight line connecting a and b not containing the endpointsMathworldPlanetmath), such that


where and are the real ( and imaginary partsMathworldPlanetmath of a complex numberMathworldPlanetmathPlanetmath, respectively.


  • 1 J.-Cl. Evard, F. Jafari, A Complex Rolle’s Theorem, American Mathematical Monthly, Vol. 99, Issue 9, (Nov. 1992), pp. 858-861.
Title complex mean-value theorem
Canonical name ComplexMeanvalueTheorem
Date of creation 2013-03-22 13:49:02
Last modified on 2013-03-22 13:49:02
Owner matte (1858)
Last modified by matte (1858)
Numerical id 7
Author matte (1858)
Entry type Theorem
Classification msc 26A06