On Some Cauchy Type Mean-Value Theorems with Applications

Uğur Selamet Kırmacı

doi:10.33434/cams.1503610

EN

On Some Cauchy Type Mean-Value Theorems with Applications

Abstract

Some Cauchy-type mean-value theorems for Chebychev’s inequality, Steffensen’s inequality, midpoint rule, and Simpson’s rule are presented. Furthermore, we give some applications for the obtained results using the exponential and logarithmic functions, their Taylor polynomials, and some trigonometric functions. Further, we obtain some exponential, logarithmic, and trigonometric equations and give two inequalities for midpoint and Simpson’s rules.

Keywords

Cauchy mean-value theorem, Chebychev’s inequality, Midpoint rule, Steffensen’s inequality, Simpson’s rule

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Uğur Selamet Kırmacı ^*
0000-0002-8177-6649
Türkiye

Early Pub Date

September 8, 2024

Publication Date

September 29, 2024

Submission Date

June 23, 2024

Acceptance Date

September 6, 2024

Published in Issue

Year 2024 Volume: 7 Number: 3

DOI

https://doi.org/10.33434/cams.1503610

IZ

https://izlik.org/JA46LN84KP

APA

Kırmacı, U. S. (2024). On Some Cauchy Type Mean-Value Theorems with Applications. Communications in Advanced Mathematical Sciences, 7(3), 147-156. https://doi.org/10.33434/cams.1503610

AMA

1.Kırmacı US. On Some Cauchy Type Mean-Value Theorems with Applications. Communications in Advanced Mathematical Sciences. 2024;7(3):147-156. doi:10.33434/cams.1503610

Chicago

Kırmacı, Uğur Selamet. 2024. “On Some Cauchy Type Mean-Value Theorems With Applications”. Communications in Advanced Mathematical Sciences 7 (3): 147-56. https://doi.org/10.33434/cams.1503610.

EndNote

Kırmacı US (September 1, 2024) On Some Cauchy Type Mean-Value Theorems with Applications. Communications in Advanced Mathematical Sciences 7 3 147–156.

IEEE

[1]U. S. Kırmacı, “On Some Cauchy Type Mean-Value Theorems with Applications”, Communications in Advanced Mathematical Sciences, vol. 7, no. 3, pp. 147–156, Sept. 2024, doi: 10.33434/cams.1503610.

ISNAD

Kırmacı, Uğur Selamet. “On Some Cauchy Type Mean-Value Theorems With Applications”. Communications in Advanced Mathematical Sciences 7/3 (September 1, 2024): 147-156. https://doi.org/10.33434/cams.1503610.

JAMA

1.Kırmacı US. On Some Cauchy Type Mean-Value Theorems with Applications. Communications in Advanced Mathematical Sciences. 2024;7:147–156.

MLA

Kırmacı, Uğur Selamet. “On Some Cauchy Type Mean-Value Theorems With Applications”. Communications in Advanced Mathematical Sciences, vol. 7, no. 3, Sept. 2024, pp. 147-56, doi:10.33434/cams.1503610.

Vancouver

1.Uğur Selamet Kırmacı. On Some Cauchy Type Mean-Value Theorems with Applications. Communications in Advanced Mathematical Sciences. 2024 Sep. 1;7(3):147-56. doi:10.33434/cams.1503610

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Mathematical Sciences and Applications E-Notes

https://doi.org/10.36753/mathenot.1500238

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