Abstract
References
- [1] Dragomir, S.S., Pečarić, J. and Persson, L.E., Some inequalities of Hadamard type, Soochow J. Math., 21 (1995) 335-341.
- [2] Dragomir, S.S. and Mond, B., Integral inequalities of Hadamard’s type for log-convex functions, Demonstration Math., 2 (1998) 354-364.
- [3] Noor, M.A., Noor, K.I. and Awan, M.U., Some characterizations of harmonically log-convex functions, Proc. Jangjeon Math. Soc., 17(1) (2014) 51-61.
- [4] Noor, M.A., Noor, K.I. and Awan, M.U., Some integral inequalities for harmonically logarithmic -convex functions, Preprint, (2014).
- [5] Noor, M.A., Noor, K.I., Awan, M.U. and Khan, S., Fractional Hermite-Hadamard inequalities for some new classes of Godunova-Levin functions, Appl. Math. Infor. Sci., 8(6) (2014).
- [6] Noor, M.A., Noor, K.I., Awan, M.U. and Costache, S., Some integral inequalities for harmonically -convex functions, U. P. B. Sci. Bull., Series A., 77(1) (2015) 5-16.
- [7] Sarikaya, M.Z., Saglam, A. and Yildirim, H., On some Hadamard-type inequalities for -convex functions, Jour. Math. Ineq., 2(3) (2008) 335-341.
- [8] Sarikaya, M.Z., Set, E. and Ozdemir, M.E., On some new inequalities of Hadamard type involving -convex functions, Acta Math. Univ. Comenianae, 2 (2010) 265-272.
- [9] Varosanec, S., On -convexity, Jour. Math. Anal. Appl., 326 (2007) 303-311.
- [10] http://arxiv.org/abs/1303.6089, (25.03.2013).
Abstract
In this study, we derived a new integral identity for differentiable functions. However, we get new inequalities which is well known as Hermite-Hadamard (H-H) type by using the integral identity, which unifies the class of new and known harmonically convex functions. Moreover, in this study, the properties of first and second kind harmonically s-convex and harmonically s-Godunova-Levin functions are studied and some special cases are also dealt. Some important inferences are made at this study for supporting the results that obtained for classes of harmonically convex functions in previous studies.
Keywords
Convex function Harmonically convex function Harmonically h-convex function Hermite-Hadamard inequality
References
- [1] Dragomir, S.S., Pečarić, J. and Persson, L.E., Some inequalities of Hadamard type, Soochow J. Math., 21 (1995) 335-341.
- [2] Dragomir, S.S. and Mond, B., Integral inequalities of Hadamard’s type for log-convex functions, Demonstration Math., 2 (1998) 354-364.
- [3] Noor, M.A., Noor, K.I. and Awan, M.U., Some characterizations of harmonically log-convex functions, Proc. Jangjeon Math. Soc., 17(1) (2014) 51-61.
- [4] Noor, M.A., Noor, K.I. and Awan, M.U., Some integral inequalities for harmonically logarithmic -convex functions, Preprint, (2014).
- [5] Noor, M.A., Noor, K.I., Awan, M.U. and Khan, S., Fractional Hermite-Hadamard inequalities for some new classes of Godunova-Levin functions, Appl. Math. Infor. Sci., 8(6) (2014).
- [6] Noor, M.A., Noor, K.I., Awan, M.U. and Costache, S., Some integral inequalities for harmonically -convex functions, U. P. B. Sci. Bull., Series A., 77(1) (2015) 5-16.
- [7] Sarikaya, M.Z., Saglam, A. and Yildirim, H., On some Hadamard-type inequalities for -convex functions, Jour. Math. Ineq., 2(3) (2008) 335-341.
- [8] Sarikaya, M.Z., Set, E. and Ozdemir, M.E., On some new inequalities of Hadamard type involving -convex functions, Acta Math. Univ. Comenianae, 2 (2010) 265-272.
- [9] Varosanec, S., On -convexity, Jour. Math. Anal. Appl., 326 (2007) 303-311.
- [10] http://arxiv.org/abs/1303.6089, (25.03.2013).
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | March 22, 2020 |
| Submission Date | March 11, 2019 |
| Acceptance Date | June 27, 2019 |
| Published in Issue | Year 2020Volume: 41 Issue: 1 |