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The mean value theorem and analytic functions of a complex variable

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
324
Issue
1
Identifiers
DOI: 10.1016/j.jmaa.2005.11.049
Keywords
  • Mean Value Theorem
  • Entire Functions
  • Quadrinomials
  • Univalent Functions
Disciplines
  • Mathematics

Abstract

Abstract The mean value theorem for real-valued differentiable functions defined on an interval is one of the most fundamental results in Analysis. When it comes to complex-valued functions the theorem fails even if the function is differentiable throughout the complex plane. we illustrate this by means of examples and also present three results of a positive nature.

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