Research Article
BibTex RIS Cite
Year 2019, Volume: 4 Issue: 1, 30 - 38, 16.05.2019

Abstract

References

  • [1] J. Hadamard, Étude sur les propriétés des fonctions entières et en particulier d.une function considerée par Riemann, J. Math Pures Appl., 58 (1893), 171-215.
  • [2] M.W. Alomari, A generalization of Hermite–Hadamard’s inequality, Kragujevac J. Math., 41 (2) (2017), 313-328.
  • [3] S.S. Dragomir, On Hadamards inequality for convex functions on the coordinates in a rectangle from the plane, Taiwanese J. Math., 4 (2001), 775–788.
  • [4] E.R. Mwaeze, Generalized Hermite–Hadamard’s inequality for functions convex on the coordinates. Applied Mathematics E-Notes, 18 (2018), 275-283.
  • [5] S.S. Dragomir, Two Mappings in Connection to Hadamard’s Inequalities, Journal of Mathematıcal Analysis and Applications 167 (1992), 49-56.
  • [6] G.S. Yang, M.C Hong, A note on Hadamard’s inequality, Tamkang J. Math. 28(1) (1997), 33–37.
  • [7] X. Gao, A Note on the Hermite–Hadamard Inequality, Journal Of Mathematical Inequalities, 4(4) (2010), 587–591.
  • [8] İ. İşcan, Hermite-Hadamard Inequalities for Harmonically Convex Functions. Hacet. J. Math. Stat. 43 (6) (2014), 935-942.
  • [9] M.A. Noor, KI. Noor and M.U. Awan, Integral inequalities for coordinated harmonically convex functions, Complex Var. Elliptic Equat., 60(6) (2015), 776–786.
  • [10] M.A. Noor, K.I. Noor and M. U. Awan. Some characterizations of harmonically log-convex functions. Proc. Jangjeon. Math. Soc., 17(1) (2014), 51-61.
  • [11] M.A. Noor, K I. Noor, M.U. Awan and S. Costache, Some integral inequalities for harmonically h-convex functions. U.P.B. Sci. Bull. Serai A, 77(1) (2015), 5-16.
  • [12] M. A. Noor, K. I. Noor and S. Iftikhar, Hermite-Hadamard inequalities for harmonic nonconvex functions, MAGNT Research Report, 4(1) (2016), 24-40.
  • [13] J.M. Viloria and M.V. Cortez, Hermite-Hadamard type inequalities for harmonically convex functions on n-coordinates, Appl. Math. Inf. Sci. Lett., 6(2) (2018), 1-6.

Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities

Year 2019, Volume: 4 Issue: 1, 30 - 38, 16.05.2019

Abstract

In
this study, we studied on the harmonically convexity of functions. Firstly, we
obtained some new generalized Hadamard’s type and Ostrowski’s type inequalities

for
these functions on the real number line.
Besides, we generalized the above mentioned inequalities using two-dimensional
operator for harmonically convex functions.

References

  • [1] J. Hadamard, Étude sur les propriétés des fonctions entières et en particulier d.une function considerée par Riemann, J. Math Pures Appl., 58 (1893), 171-215.
  • [2] M.W. Alomari, A generalization of Hermite–Hadamard’s inequality, Kragujevac J. Math., 41 (2) (2017), 313-328.
  • [3] S.S. Dragomir, On Hadamards inequality for convex functions on the coordinates in a rectangle from the plane, Taiwanese J. Math., 4 (2001), 775–788.
  • [4] E.R. Mwaeze, Generalized Hermite–Hadamard’s inequality for functions convex on the coordinates. Applied Mathematics E-Notes, 18 (2018), 275-283.
  • [5] S.S. Dragomir, Two Mappings in Connection to Hadamard’s Inequalities, Journal of Mathematıcal Analysis and Applications 167 (1992), 49-56.
  • [6] G.S. Yang, M.C Hong, A note on Hadamard’s inequality, Tamkang J. Math. 28(1) (1997), 33–37.
  • [7] X. Gao, A Note on the Hermite–Hadamard Inequality, Journal Of Mathematical Inequalities, 4(4) (2010), 587–591.
  • [8] İ. İşcan, Hermite-Hadamard Inequalities for Harmonically Convex Functions. Hacet. J. Math. Stat. 43 (6) (2014), 935-942.
  • [9] M.A. Noor, KI. Noor and M.U. Awan, Integral inequalities for coordinated harmonically convex functions, Complex Var. Elliptic Equat., 60(6) (2015), 776–786.
  • [10] M.A. Noor, K.I. Noor and M. U. Awan. Some characterizations of harmonically log-convex functions. Proc. Jangjeon. Math. Soc., 17(1) (2014), 51-61.
  • [11] M.A. Noor, K I. Noor, M.U. Awan and S. Costache, Some integral inequalities for harmonically h-convex functions. U.P.B. Sci. Bull. Serai A, 77(1) (2015), 5-16.
  • [12] M. A. Noor, K. I. Noor and S. Iftikhar, Hermite-Hadamard inequalities for harmonic nonconvex functions, MAGNT Research Report, 4(1) (2016), 24-40.
  • [13] J.M. Viloria and M.V. Cortez, Hermite-Hadamard type inequalities for harmonically convex functions on n-coordinates, Appl. Math. Inf. Sci. Lett., 6(2) (2018), 1-6.
There are 13 citations in total.

Details

Primary Language English
Journal Section Volume IV, Issue I, 2019
Authors

Fatma Buğlem Yalçın 0000-0003-4276-1820

Nurgül Okur 0000-0002-2544-7752

Publication Date May 16, 2019
Published in Issue Year 2019 Volume: 4 Issue: 1

Cite

APA Yalçın, F. B., & Okur, N. (2019). Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities. Turkish Journal of Science, 4(1), 30-38.
AMA Yalçın FB, Okur N. Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities. TJOS. May 2019;4(1):30-38.
Chicago Yalçın, Fatma Buğlem, and Nurgül Okur. “Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities”. Turkish Journal of Science 4, no. 1 (May 2019): 30-38.
EndNote Yalçın FB, Okur N (May 1, 2019) Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities. Turkish Journal of Science 4 1 30–38.
IEEE F. B. Yalçın and N. Okur, “Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities”, TJOS, vol. 4, no. 1, pp. 30–38, 2019.
ISNAD Yalçın, Fatma Buğlem - Okur, Nurgül. “Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities”. Turkish Journal of Science 4/1 (May 2019), 30-38.
JAMA Yalçın FB, Okur N. Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities. TJOS. 2019;4:30–38.
MLA Yalçın, Fatma Buğlem and Nurgül Okur. “Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities”. Turkish Journal of Science, vol. 4, no. 1, 2019, pp. 30-38.
Vancouver Yalçın FB, Okur N. Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities. TJOS. 2019;4(1):30-8.