Some variants of Lagrange's mean value theorem

Authors

  • German Lozada-Cruz Departamento de Matemática, Instituto de Biociéncias, Letras e Cincias Exatas (IBILCE) - Universidade Estadual Paulista (UNESP), 15054-000 Sao José do Rio Preto, Sao Paulo, Brazil. http://orcid.org/0000-0003-2860-954X

DOI:

https://doi.org/10.17268/sel.mat.2020.01.13

Keywords:

Flett's theorem, Myers' theorem, Sahoo-Riedel's theorem, Cakmak-Tiryaki's theorem

Abstract

In this note we prove some variants of Lagrange’s mean value theorem. The main tools to prove these results are some elementary auxiliary functions.

References

Cakmak D, Tiryaki A. Mean value theorem for holomorphic functions. 2012; 2012(34):1-6.

Flett T. A mean value problem. Math. Gazette. 1958; 42: 38-39.

Lang S. Undergraduate Analysis. 2a ed. Undergraduate Texts in Mathematics. New York: Springer-Verlag, 2005.

Mercer P. On a mean value theorem. The College Math. J. 2002; 33(1):46-47.

Mohapatra A. Cauchy type generalizations of holomorphic mean value theorems. Electron. J. Diff. Equ. 2012; 184:1-6.

Myers R. Some elementary results related to the mean value theorem. The Two-Year College Mathematics Journal. 1997; 8(1):51-53.

Protter M, Morrey C. A first course in real analysis. 2a ed. Undergraduate Texts in Mathematics, New York: Springer-Verlag Inc., 1991.

Sahoo P, Riedel T. Mean Value Theorems and Functional Equations. NJ: World Scientific, River Edge, 1998.

Tong J. A new auxiliary function for the mean value theorem. Journal of the North Carolina Academy of Science. 2005; 121(4):174-176.

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Published

2020-07-25

How to Cite

Lozada-Cruz, G. (2020). Some variants of Lagrange’s mean value theorem. Selecciones Matemáticas, 7(01), 144-150. https://doi.org/10.17268/sel.mat.2020.01.13

Issue

Vol. 7 No. 01 (2020): January - July

Section

Articles

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