THE MEAN VALUE THEOREM FOR HOLOMORPHIC FUNCTIONS OF A COMPLEX VARIABLE

Authors

  • Luu Thi Thu Huyen Đại học Hùng Vương
  • Luu Phuong Linh Hung Vuong High Quality High School

DOI:

https://doi.org/10.51453/2354-1431/2021/549

Keywords:

Mean value theorem, Mean value theorem in , Complex Rolle’s theorem, Flett’s theorem, Myers’s theorem

Abstract

The mean value theorem is one of the most fundamental results in real analysis. However, it fails for analytically complex one-factor functions even if the function is differentiable throughout  the complex plane. In this paper, we specify this with some specific examples, and we also show the equivalence between Rolle's theorem and Mean value theorem in the complex plane.

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References

[1] J.C. Evard and F. Jafari, A complex Rolle’s theorem, Amer. Math. Monthly, 99 (1992), 858-861.

[2] T.M. Flett, A mean value theorem, Math. Gazette, 42 (1958), 38-39.

[3] Y. Kaya, Complex Rolle and Mean Value Theorems, MSc Thesis, Balıkesir University,

(2015).

[4] R.E. Myers, Some elementary results related to the mean value theorem, The twoyear college Mathematics journal, 8(1) (1977), 51-53.

[5] M.A. Qazi, The mean value theorem and analytic functions of a complex variable, J.

Math. Anal. Appl. 324 (2006) 30 – 38.

[6] P.K. Sahoo and T.R. Riedel, Mean value theorem and functional equations, World

Scientific, River Edge, New Jersey, 1998.

[7] Sümeyra Uçar and Nihal Özgür, Complex conformable Rolle’s and Mean Value

Theorems, Mathematical Sciences, Vol. 14, no. 3, Sept. 2020.

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Published

2022-04-12

How to Cite

Lưu Thị, T. H., & Lưu Phương, L. (2022). THE MEAN VALUE THEOREM FOR HOLOMORPHIC FUNCTIONS OF A COMPLEX VARIABLE. SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY, 7(24). https://doi.org/10.51453/2354-1431/2021/549

Issue

Vol. 7 No. 24 (2021): No. 24, DECEMBER-2021

Section

Natural Science and Technology

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