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Year 2020, , 38 - 43, 25.03.2020
https://doi.org/10.32323/ujma.571525

Abstract

References

  • [1] S.S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11(5) (1998), 91-95.
  • [2] S.S. Dragomir, Refinements of the Hermite-Hadamard integral inequality for log-convex functions, Aust. Math. Soc. Gaz. 28(3) (2001), 129-134.
  • [3] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Its Applications, RGMIA Monograph 2002.
  • [4] S.S. Dragomir, J. Pecaric and LE.Persson, Some inequalities of Hadamard Type, Soochow Journal of Mathematics, 21(3) (2001), pp. 335-341.
  • [5] J. Hadamard, Etude sur les proprietes des fonctions entieres en particulier d’une fonction consideree par Riemann, J. Math. Pures Appl. 58 (1893), 171-215.
  • [6] İ. İşcan, New refinements for integral and sum forms of H¨older inequality, Journal of Inequalities and Applications, (2019) 2019:304
  • [7] H. Kadakal, Hermite-Hadamard type inequalities for trigonometrically convex functions, Scientific Studies and Research. Series Mathematics and Informatics, 28(2) (2018), 19-28.
  • [8] M. Kadakal, İ. İşcan, H. Kadakal and K. Bekar, On improvements of some integral inequalities, Researchgate, DOI: 10.13140/RG.2.2.15052.46724, Preprint, January 2019.
  • [9] M. Kadakal, H. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable s-convex functions in the first sense, Turkish Journal of Analysis and Number Theory, 5(2) (2017), 63-68.
  • [10] S. Maden, H. Kadakal, M. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable convex and concave functions, Journal of Nonlinear Sciences and Applications, 10(12) (2017), 6141-6148.
  • [11] F. Usta, H. Budak and M. Z. Sarıkaya, Montgomery identities and Ostrowski type inequalities for fractional integral operators, Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matematicas, 113(2) (2019), 1059-1080
  • [12] F. Usta, H. Budak and M. Z. Sarıkaya, Some New Chebyshev Type Inequalities Utilizing Generalized Fractional Integral Operators, AIMS Mathematics, 5(2) (2020) 1147-1161.
  • [13] F. Usta, H. Budak, M. Z. Sarıkaya and E. Set, On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators, Filomat, 32(6) (2018), 2153–2171.
  • [14] S. Varosanec, On h-convexity, J. Math. Anal. Appl. 326 (2007) 303-311.
  • [15] G. Zabandan, A new refinement of the Hermite-Hadamard inequality for convex functions, J. Inequal. Pure Appl. Math. 10(2) (2009), Article ID 45.

Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities

Year 2020, , 38 - 43, 25.03.2020
https://doi.org/10.32323/ujma.571525

Abstract

In this paper, using Hölder-İşcan and improved power-mean integral inequalities and together with an integral identity, we obtain Hadamard type inequalities for functions whose second derivatives in absolute value at certain power are trigonometrically convex functions. In addition, we prove that our results give better approach than previous results.

References

  • [1] S.S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11(5) (1998), 91-95.
  • [2] S.S. Dragomir, Refinements of the Hermite-Hadamard integral inequality for log-convex functions, Aust. Math. Soc. Gaz. 28(3) (2001), 129-134.
  • [3] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Its Applications, RGMIA Monograph 2002.
  • [4] S.S. Dragomir, J. Pecaric and LE.Persson, Some inequalities of Hadamard Type, Soochow Journal of Mathematics, 21(3) (2001), pp. 335-341.
  • [5] J. Hadamard, Etude sur les proprietes des fonctions entieres en particulier d’une fonction consideree par Riemann, J. Math. Pures Appl. 58 (1893), 171-215.
  • [6] İ. İşcan, New refinements for integral and sum forms of H¨older inequality, Journal of Inequalities and Applications, (2019) 2019:304
  • [7] H. Kadakal, Hermite-Hadamard type inequalities for trigonometrically convex functions, Scientific Studies and Research. Series Mathematics and Informatics, 28(2) (2018), 19-28.
  • [8] M. Kadakal, İ. İşcan, H. Kadakal and K. Bekar, On improvements of some integral inequalities, Researchgate, DOI: 10.13140/RG.2.2.15052.46724, Preprint, January 2019.
  • [9] M. Kadakal, H. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable s-convex functions in the first sense, Turkish Journal of Analysis and Number Theory, 5(2) (2017), 63-68.
  • [10] S. Maden, H. Kadakal, M. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable convex and concave functions, Journal of Nonlinear Sciences and Applications, 10(12) (2017), 6141-6148.
  • [11] F. Usta, H. Budak and M. Z. Sarıkaya, Montgomery identities and Ostrowski type inequalities for fractional integral operators, Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matematicas, 113(2) (2019), 1059-1080
  • [12] F. Usta, H. Budak and M. Z. Sarıkaya, Some New Chebyshev Type Inequalities Utilizing Generalized Fractional Integral Operators, AIMS Mathematics, 5(2) (2020) 1147-1161.
  • [13] F. Usta, H. Budak, M. Z. Sarıkaya and E. Set, On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators, Filomat, 32(6) (2018), 2153–2171.
  • [14] S. Varosanec, On h-convexity, J. Math. Anal. Appl. 326 (2007) 303-311.
  • [15] G. Zabandan, A new refinement of the Hermite-Hadamard inequality for convex functions, J. Inequal. Pure Appl. Math. 10(2) (2009), Article ID 45.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mahir Kadakal 0000-0002-0240-918X

Publication Date March 25, 2020
Submission Date May 29, 2019
Acceptance Date February 25, 2020
Published in Issue Year 2020

Cite

APA Kadakal, M. (2020). Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities. Universal Journal of Mathematics and Applications, 3(1), 38-43. https://doi.org/10.32323/ujma.571525
AMA Kadakal M. Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities. Univ. J. Math. Appl. March 2020;3(1):38-43. doi:10.32323/ujma.571525
Chicago Kadakal, Mahir. “Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities”. Universal Journal of Mathematics and Applications 3, no. 1 (March 2020): 38-43. https://doi.org/10.32323/ujma.571525.
EndNote Kadakal M (March 1, 2020) Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities. Universal Journal of Mathematics and Applications 3 1 38–43.
IEEE M. Kadakal, “Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities”, Univ. J. Math. Appl., vol. 3, no. 1, pp. 38–43, 2020, doi: 10.32323/ujma.571525.
ISNAD Kadakal, Mahir. “Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities”. Universal Journal of Mathematics and Applications 3/1 (March 2020), 38-43. https://doi.org/10.32323/ujma.571525.
JAMA Kadakal M. Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities. Univ. J. Math. Appl. 2020;3:38–43.
MLA Kadakal, Mahir. “Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities”. Universal Journal of Mathematics and Applications, vol. 3, no. 1, 2020, pp. 38-43, doi:10.32323/ujma.571525.
Vancouver Kadakal M. Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities. Univ. J. Math. Appl. 2020;3(1):38-43.

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