Research Article

Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities

Volume: 4 Number: 1 May 16, 2019
EN

Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities

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.

Keywords

References

  1. [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. [2] M.W. Alomari, A generalization of Hermite–Hadamard’s inequality, Kragujevac J. Math., 41 (2) (2017), 313-328.
  3. [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. [4] E.R. Mwaeze, Generalized Hermite–Hadamard’s inequality for functions convex on the coordinates. Applied Mathematics E-Notes, 18 (2018), 275-283.
  5. [5] S.S. Dragomir, Two Mappings in Connection to Hadamard’s Inequalities, Journal of Mathematıcal Analysis and Applications 167 (1992), 49-56.
  6. [6] G.S. Yang, M.C Hong, A note on Hadamard’s inequality, Tamkang J. Math. 28(1) (1997), 33–37.
  7. [7] X. Gao, A Note on the Hermite–Hadamard Inequality, Journal Of Mathematical Inequalities, 4(4) (2010), 587–591.
  8. [8] İ. İşcan, Hermite-Hadamard Inequalities for Harmonically Convex Functions. Hacet. J. Math. Stat. 43 (6) (2014), 935-942.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Publication Date

May 16, 2019

Submission Date

March 12, 2019

Acceptance Date

April 25, 2019

Published in Issue

Year 2019 Volume: 4 Number: 1

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. https://izlik.org/JA57LF23KP
AMA
1.Yalçın FB, Okur N. Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities. TJOS. 2019;4(1):30-38. https://izlik.org/JA57LF23KP
Chicago
Yalçın, Fatma Buğlem, and Nurgül Okur. 2019. “Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities”. Turkish Journal of Science 4 (1): 30-38. https://izlik.org/JA57LF23KP.
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
[1]F. B. Yalçın and N. Okur, “Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities”, TJOS, vol. 4, no. 1, pp. 30–38, May 2019, [Online]. Available: https://izlik.org/JA57LF23KP
ISNAD
Yalçın, Fatma Buğlem - Okur, Nurgül. “Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities”. Turkish Journal of Science 4/1 (May 1, 2019): 30-38. https://izlik.org/JA57LF23KP.
JAMA
1.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, May 2019, pp. 30-38, https://izlik.org/JA57LF23KP.
Vancouver
1.Fatma Buğlem Yalçın, Nurgül Okur. Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities. TJOS [Internet]. 2019 May 1;4(1):30-8. Available from: https://izlik.org/JA57LF23KP