Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2022, Cilt: 43 Sayı: 3, 497 - 503, 30.09.2022

Huriye Kadakal

https://doi.org/10.17776/csj.1110051
Cited By: 5

Öz

Destekleyen Kurum

Bayburt Üniversitesi BAP projeleri birimi

Proje Numarası

BAP [2022/69002-03]

Kaynakça

  • [1] Dragomir S.S., Pearce C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, (2000).
  • [2] Kadakal H., New Inequalities for Strongly r-Convex Functions, Journal of Function Spaces, 2019 (2019) 10 p.
  • [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.
  • [11] Kadakal H., Hermite-Hadamard type inequalities for two times differentiable arithmetic-harmonically convex functions, Cumhuriyet Science Journal, 40(3) (2019) 670-678.
  • [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.
  • [13] Kadakal H., On refinements of some integral inequalities using improved power-mean integral inequalities, Numerical Methods for Partial Differential Equations, 36(6) (2020) 1555-1565.
  • [14] Kadakal H., Hermite-Hadamard type inequalities for subadditive functions, AIMS Mathematics, 5(2) (2020) 930-939.
  • [15] Kadakal M., Geometric trigonometrically convexity and better approximations, Numerical Methods for Partial Differential Equations, 36(6) (2020) 1830-1844.
  • [16] Kadakal M., İşcan İ., Exponential type convexity and some related inequalities, Journal of Inequalities and Applications, 2020(1) (2020) 1-9.
  • [17] Kadakal M., et al. On improvements of some integral inequalities, Honam Mathematical Journal, 43(3) (2021) 441-452.
  • [18] Kadakal H., Kadakal M., İşcan İ., Some new integral inequalities for N-times differentiable R-convex and R-concave functions, Miskolc Mathematical Notes, 20(2) (2019) 997-1011.
  • [19] Özcan S., İşcan İ., Some new Hermite-Hadamard type inequalities for s-convex functions and their applications, Journal of inequalities and applications, 2019(1) (2019) 1-11.
  • [20] Özcan S., Some integral inequalities for harmonically-convex functions, Journal of Function Spaces, 2019 (2019).
  • [21] Toplu T., Kadakal M., İşcan İ., On n-polynomial convexity and some related inequalities, AIMS Math., 5(2) (2020) 1304-1318.

Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions

Yıl 2022, Cilt: 43 Sayı: 3, 497 - 503, 30.09.2022

Huriye Kadakal

https://doi.org/10.17776/csj.1110051
Cited By: 5

Öz

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.

Anahtar Kelimeler

Convex function Arithmetic-harmonically convex function Hermite-Hadamard and Bullen type inequality.

Proje Numarası

BAP [2022/69002-03]

Kaynakça

  • [1] Dragomir S.S., Pearce C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, (2000).
  • [2] Kadakal H., New Inequalities for Strongly r-Convex Functions, Journal of Function Spaces, 2019 (2019) 10 p.
  • [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.
  • [11] Kadakal H., Hermite-Hadamard type inequalities for two times differentiable arithmetic-harmonically convex functions, Cumhuriyet Science Journal, 40(3) (2019) 670-678.
  • [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.
  • [13] Kadakal H., On refinements of some integral inequalities using improved power-mean integral inequalities, Numerical Methods for Partial Differential Equations, 36(6) (2020) 1555-1565.
  • [14] Kadakal H., Hermite-Hadamard type inequalities for subadditive functions, AIMS Mathematics, 5(2) (2020) 930-939.
  • [15] Kadakal M., Geometric trigonometrically convexity and better approximations, Numerical Methods for Partial Differential Equations, 36(6) (2020) 1830-1844.
  • [16] Kadakal M., İşcan İ., Exponential type convexity and some related inequalities, Journal of Inequalities and Applications, 2020(1) (2020) 1-9.
  • [17] Kadakal M., et al. On improvements of some integral inequalities, Honam Mathematical Journal, 43(3) (2021) 441-452.
  • [18] Kadakal H., Kadakal M., İşcan İ., Some new integral inequalities for N-times differentiable R-convex and R-concave functions, Miskolc Mathematical Notes, 20(2) (2019) 997-1011.
  • [19] Özcan S., İşcan İ., Some new Hermite-Hadamard type inequalities for s-convex functions and their applications, Journal of inequalities and applications, 2019(1) (2019) 1-11.
  • [20] Özcan S., Some integral inequalities for harmonically-convex functions, Journal of Function Spaces, 2019 (2019).
  • [21] Toplu T., Kadakal M., İşcan İ., On n-polynomial convexity and some related inequalities, AIMS Math., 5(2) (2020) 1304-1318.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Natural Sciences
Yazarlar

Huriye Kadakal 0000-0002-0304-7192

Proje Numarası BAP [2022/69002-03]
Yayımlanma Tarihi 30 Eylül 2022
Gönderilme Tarihi 27 Nisan 2022
Kabul Tarihi 15 Eylül 2022
Yayımlandığı Sayı Yıl 2022Cilt: 43 Sayı: 3

Kaynak Göster

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

An investigation into inequalities obtained through the new Lemma for exponential type convex functions
Filomat
https://doi.org/10.2298/FIL2315149Y
Fractional integral inequalities for the s-(κ,H)-convex function
Analysis
https://doi.org/10.1515/anly-2023-0061
Earthquake convexity and some new related inequalities
Journal of Applied Analysis
https://doi.org/10.1515/jaa-2023-0046
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
STRONGLY HYPERBOLIC TYPE CONVEXITY AND SOME NEW INEQUALITIES
Journal of Science and Arts
https://doi.org/10.46939/J.Sci.Arts-23.3-a02
 Kapak Resmi İndir