Real Analysis Exchange

Another application of Rolles's theorem.

F. S. Cater

Full-text: Open access

Abstract

We find an analogue of Rolle's Theorem in (real variable) calculus for continuous complex valued functions defined on convex subsets of the complex plane.

Article information

Source
Real Anal. Exchange Volume 30, Number 2 (2004), 795- 798 .

Dates
First available: 15 October 2005

Permanent link to this document
http://projecteuclid.org/euclid.rae/1129416482

Mathematical Reviews number (MathSciNet)
MR2177436

Subjects
Primary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]
Secondary: 30D20: Entire functions, general theory

Keywords
convex set directional derivative analytic function

Citation

Cater, F. S. Another application of Rolles's theorem. Real Analysis Exchange 30 (2004), no. 2, 795-- 798. http://projecteuclid.org/euclid.rae/1129416482.


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References

  • S. Lang, Complex Analysis, 2nd ed., Springer-Verlag, New York, 1985.
  • A. Wayne Roberts, Introductory Calculus, 2nd ed., Academic Press, New York, 1972.