Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities

Yıl 2019, Cilt: 4 Sayı: 1, 30 - 38, 16.05.2019

Fatma Buğlem Yalçın Nurgül Okur

Öz

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.

Anahtar Kelimeler

harmonically convex function, Hermite-Hadamard type inequalities, Ostrowski’s type inequalities

Kaynakça

• [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.