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Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions

Year 2022, Volume 43, Issue 3, 497 - 503, 30.09.2022
https://doi.org/10.17776/csj.1110051

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.

References

  • [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.

Year 2022, Volume 43, Issue 3, 497 - 503, 30.09.2022
https://doi.org/10.17776/csj.1110051

Abstract

References

  • [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.

Details

Primary Language English
Subjects Mathematics
Journal Section Natural Sciences
Authors

Huriye KADAKAL> (Primary Author)
BAYBURT ÜNİVERSİTESİ, BAYBURT EĞİTİM FAKÜLTESİ
0000-0002-0304-7192
Türkiye

Supporting Institution Bayburt Üniversitesi BAP projeleri birimi
Project Number BAP [2022/69002-03]
Publication Date September 30, 2022
Application Date April 27, 2022
Acceptance Date September 15, 2022
Published in Issue Year 2022, Volume 43, Issue 3

Cite

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