Some generalized inequalities of Hermite-Hadamard type for strongly s-convex functions

Abstract

In this paper, some new generalized results related to the left-hand and the right-hand of the Hermite-Hadamard inequalities for the class of functions whose derivatives are strongly-convex functions in the second sense are established. Some previous results are also recaptured as a special case.

Keywords

• Hadamard type inequalities,Hölder inequality

References

1. H. Angulo, J. Gimenez, A. M. Moros, and K. Nikodem, On strongly h-convex function, Ann. Funct. Anal. 2(2), 2011, 85–91.
2. M. K. Bakula and J. Pečarić, Note on some Hadamard-type inequalities, Journal of Inequalities in Pure and Applied Mathematics, vol. 5, no. 3, article 74, 2004.
3. M. V. Cortez, Relative strongly h-convex functions and integral inequalities, Appl. Math. Inf. Sci. Lett. 4, No. 2, 1-7 (2016).
4. S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
5. S. S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. lett., 11(5) (1998), 91-95.
6. H. Hudzik, L. Maligranda, Some remarks on s-convex functions. Aequ. Math. 48, 100-111 (1994).
7. M. E. Kiris and M. Z. Sarikaya, Some generalized inequalities for Hermite-Hadamard’s integral inequalities and applications, submited (2015).
8. J. Makó and A. Házy, On strongly convex functions. Carpathian Journal of Mathematics, 32 (1). 87-95.

9. N. Merentes, K. Nikodem, Remarks on strongly convex functions, Aequationes Math. 80 (2010) 193–199.
10. K. Nikodem, Z. Pales, Characterizations of inner product spaces be strongly convex functions, Banach J. Math. Anal. 5 (2011) 83–87.
11. M. E. Özdemir, Ç. Yıldız, A. O. Akdemir and E. Set, On some inequalities for s-convex functions and applications, Journal of Inequalities and Applications 2013, 2013:333.
12. J.E. Pečarić, F. Proschan and Y.L. Tong, Convex functions, partial orderings and statistical applications, Academic Press, Boston, 1992.
13. B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restictions, Soviet Math. Dokl. 7 (1966), 72–75.
14. M. Z. Sarikaya, T. Tunc and M. K. Yildiz, Some generalized integral inequalities for convex functions and applications, AIP Conference Proceedings, 1726, 020047 (2016); doi: 10.1063/1.4945873.
15. M. Z. Sarikaya, On strongly φ_h-convex functions in inner product spaces, Arabian Journal of Mathematics, (2013) 2:295–302.
16. M. Z. Sarikaya, E. Set, M. E. Ozdemir and S. S. Dragomir, New some Hadamard’s type inequalities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2) (2012) 137-152.
17. M. Z. Sarikaya and H. Yaldiz, On Hermite Hadamard-type inequalities for strongly log-convex functions, International Journal of Modern Mathematical Sciences, 2013, 5(3): 92-98.
18. M. Z. Sarikaya and H. Yaldiz, On the Hadamard’s type inequalities for L-Lipschitzian mapping, Konuralp Journal of Mathematics, 1(2), 33-40 (2013).
19. M. Z. Sarikaya and K. Ozcelik, On Hermite-Hadamard type integral inequalities for strongly φ_h-convex functions, International Journal of Advanced Research in Engineering and Applied Sciences (IJAREAS), 1(1), pp:34-52, 2014.
20. M. Z. Sarikaya, On Hermite Hadamard-type inequalities for strongly φ-convex functions, Southeast Asian Bull. Math., 39(1) (2015) , pp: 123-132.
21. M. Z. Sarikaya, E. Set and M. E. Ozdemir, On new inequalities of Simpson’s type for s-convex functions, Computers and Mathematics with Applications 60 (2010) 2191–2199.