Some Variants of Wayment's Mean Value Theorem for Integrals

Authors

  • German Lozada-Cruz Departamento de Matemática, Instituto de Biociencias, Letras e Ciencias Exatas (IBILCE) – Universidade Estadual Paulista (UNESP), 15054-000 Sao José do Rio Preto, Sao Paulo, Brazil.

DOI:

https://doi.org/10.17268/sel.mat.2025.01.05

Keywords:

Flett's theorem, Myers' theorem, Wayment's theorem

Abstract

This note deals with some variants of Wayment’s Mean Value Theorem for integrals. Our approach is rather elementary and does not use advanced techniques from analysis. The simple auxiliary functions were used to prove the results.

References

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

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

Myers RE. Some elementary results related to the mean value theorem, The two-year college Mathematics Journal 8(1977).

Bougoffa L. A generalization of Wayment’s mean value theorem for integrals, The American Mathematical Monthly. 2024; 1-3.

Wayment SG. An integral mean value theorem, Math. Gazette. 1970; 54: 300-301.

Lozada-Cruz G. Some variants of Integral mean value theorem. Int. J. Math. Ed.Sci. Tech. 2021; 52(7):1124-1130.

Trench WF. Introduction to real analysis. Free Hyperlinked Edition 2.04 December 2013.

https://digitalcommons.trinity.edu/cgi/viewcontent.cgi?article=1006&context=mono

Wachnicki E. Une variante du théoreme de Cauchy de la valeur moyenne. Demonstr. Math. 2000; 33: 737-740.

Lozada-Cruz G. Some variants of Cauchy’s mean value theorem. Int. J. Math. Ed. Sci. Tech. 2020; 51(7):1155-1163.

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Published

2025-07-26

How to Cite

Lozada-Cruz, G. (2025). Some Variants of Wayment’s Mean Value Theorem for Integrals. Selecciones Matemáticas, 12(01), 62 - 66. https://doi.org/10.17268/sel.mat.2025.01.05

Issue

Vol. 12 No. 01 (2025): January - July

Section

Articles

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