Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions

Huriye Kadakal

doi:10.17776/csj.1110051

EN

Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions

Abstract

In this study, by using an integral identity, Hölder integral inequality and modulus properties we obtain some new general inequalities of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are arithmetically harmonically (AH) convex. In the last part of the article, applications including arithmetic mean, geometric mean, harmonic mean, logarithmic mean and p-logarithmic mean, which are some special means of real numbers, are given by using arithmetic harmonically convex functions.

Keywords

Supporting Institution

Bayburt Üniversitesi BAP projeleri birimi

Project Number

BAP [2022/69002-03]

References

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[3] Maden S., Kadakal H., Kadakal M., İşcan İ., Some new integral inequalities for n-times differentiable convex and concave functions, J. Nonlinear Sci. Appl., 10(12) (2017) 6141-6148.
[4] Sarikaya M.Z., Aktan N., On the generalization of some integral inequalities and their applications, Mathematical and Computer Modelling, 54 (2011) 2175-2182.
[5] Dragomir S.S., Inequalities of Hermite-Hadamard type for AH-convex functions, Stud. Univ. Babeş-Bolyai Math. 61(4) (2016) 489-502.
[6] Zhang T.Y., Qi F., Integral Inequalities of Hermite–Hadamard Type for m-AH Convex Functions, Turkish Journal of Analysis and Number Theory, 2(3) (2014) 60-64.
[7] Agarwal P., Kadakal M., İşcan İ., Chu Y.M., Better approaches for n-times differentiable convex functions, Mathematics, 8(6) (2020) 950.
[8] Bekar K., Inequalities for three-times differentiable arithmetic-harmonically functions, Turkish Journal of Analysis and Number Theory, 7(3) (2019) 85-90.

[9] İşcan İ., Kadakal H., Kadakal M., Some new integrl inequalities for n-times differentiable quasi-convex functions, Sigma Journal of Engineering and Natural Sciences, 35(3) (2017) 363-368.
[10] İşcan İ., Toplu T. and Yetgin F., Some new inequalities on generaliation of hermite-Hadamard and Bullen typeinequalities, applications to trapezoidal and midpoint formula, Kragujevac Journal of Mathematics, 45(4) (2021) 647-657.
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[12] Kadakal H., (α,m_1,m_2)-convexity and some inequalities of Hermite-Hadamard type, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2) (2019) 2128-2142.
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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Huriye Kadakal ^*
0000-0002-0304-7192
Türkiye

Publication Date

September 30, 2022

Submission Date

April 27, 2022

Acceptance Date

September 15, 2022

Published in Issue

Year 1970 Volume: 43 Number: 3

DOI

https://doi.org/10.17776/csj.1110051

IZ

https://izlik.org/JA69YE64ZU

Cite

RIS / Bibtex

APA

Kadakal, H. (2022). Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions. Cumhuriyet Science Journal, 43(3), 497-503. https://doi.org/10.17776/csj.1110051

Cited By

STRONGLY HYPERBOLIC TYPE CONVEXITY AND SOME NEW INEQUALITIES

Journal of Science and Arts

https://doi.org/10.46939/J.Sci.Arts-23.3-a02

Some novel refinements of Hermite-Hadamard and Pachpatte type integral inequalities involving a generalized preinvex function pertaining to Caputo-Fabrizio fractional integral operator

AIMS Mathematics

https://doi.org/10.3934/math.20231306

Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions

Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions

Abstract

Keywords

Öz

Supporting Institution

Project Number

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite

Cited By

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