Abstract
A new identity has been handled in this paper. It allows to derive new inequalities referring to upper estimation of the Jensen functional in the class of s, m - convex functions. Also some applications for special means are given by using new inequalities.
Keywords
Convex function s m -convex Hermite-Hadamard inequalitiy H¨older inequality power mean inequality
References
- Dragomir, S. S., Agarwal, R. P., & Barnet, N. S. (2000) Inequalities for Beta and Gamma Functions via Some Classical and New Integral Inequalities. J. Ineq. Appl., 5, (2), 103-165.
- Dragomir, S. S., & Pearce, C.E.M. (2000). Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs
- Victoria University,[ONLINE. http://rgmia.org/papers/monographs/Master.pdf]. Breckner, W. W. (1978). Stetigkeitsaussagen f¨ur eine klasse verallgemeinerter konvexer funktionen in topologischen linearen r¨aumen. Publ. Inst. Math, 23 (37), 13-20.
- Kirmaci, U. S. (2017), On Some Hermite-Hadamard Type Inequalities for Twice Differentiable (α, m)- convex functions and Applications. RGMIA Res. Rep. Coll., 20, Art. 51.
- ¨Ozdemir, M. E., Avci, M., & H. Kavurmaci. (2011). Hermite-Hadamard-type Inequalities via (α, m)- convexity. Computer and Math. with Appl., 61, 2614-2620.
- Park, J. (2011). Generalization of Ostrowski-type inequalities for differentiable real (s, m)-convex mappings. Far East J. of Math. Sci., 49(2), 157-171.
- Park, J. (2011). Ostrowski type inequalities for mappings whose derivatives are (s, m) −convex in the second sense. Far East J. of Math. Sci., 49 (2), 181-195.
- Sarikaya, M. Z., & Aktan, N. (2011). On the generalization of some integral inequalities and their applications. Math. and Comp. Modelling, 54, 2175-2182.
- Set, E., Sardari, M., ¨Ozdemir, M. E., & Rooin, J. (2012). On Generalizations of the Hadamard
- Inequality for (α, m)-Convex Functions. Kyungpook Math. J., 52, 307-317
- Toader, G.H. (1984). Some Generalisations of the Convexity. Proc. Colloq. Approx. Optim, Cluj- Napoca, 329-338, Romania.
- Dragomir, S.S. (2006). Bounds for the normalized Jensen functional. Bull. Aust. Math. Soc. 74(3), 476. uz
Abstract
References
- Dragomir, S. S., Agarwal, R. P., & Barnet, N. S. (2000) Inequalities for Beta and Gamma Functions via Some Classical and New Integral Inequalities. J. Ineq. Appl., 5, (2), 103-165.
- Dragomir, S. S., & Pearce, C.E.M. (2000). Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs
- Victoria University,[ONLINE. http://rgmia.org/papers/monographs/Master.pdf]. Breckner, W. W. (1978). Stetigkeitsaussagen f¨ur eine klasse verallgemeinerter konvexer funktionen in topologischen linearen r¨aumen. Publ. Inst. Math, 23 (37), 13-20.
- Kirmaci, U. S. (2017), On Some Hermite-Hadamard Type Inequalities for Twice Differentiable (α, m)- convex functions and Applications. RGMIA Res. Rep. Coll., 20, Art. 51.
- ¨Ozdemir, M. E., Avci, M., & H. Kavurmaci. (2011). Hermite-Hadamard-type Inequalities via (α, m)- convexity. Computer and Math. with Appl., 61, 2614-2620.
- Park, J. (2011). Generalization of Ostrowski-type inequalities for differentiable real (s, m)-convex mappings. Far East J. of Math. Sci., 49(2), 157-171.
- Park, J. (2011). Ostrowski type inequalities for mappings whose derivatives are (s, m) −convex in the second sense. Far East J. of Math. Sci., 49 (2), 181-195.
- Sarikaya, M. Z., & Aktan, N. (2011). On the generalization of some integral inequalities and their applications. Math. and Comp. Modelling, 54, 2175-2182.
- Set, E., Sardari, M., ¨Ozdemir, M. E., & Rooin, J. (2012). On Generalizations of the Hadamard
- Inequality for (α, m)-Convex Functions. Kyungpook Math. J., 52, 307-317
- Toader, G.H. (1984). Some Generalisations of the Convexity. Proc. Colloq. Approx. Optim, Cluj- Napoca, 329-338, Romania.
- Dragomir, S.S. (2006). Bounds for the normalized Jensen functional. Bull. Aust. Math. Soc. 74(3), 476. uz
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | March 1, 2020 |
| Published in Issue | Year 2020 Volume: 10 Issue: 2 |