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

Year 2017, Volume: 5 Issue: 3, 22 - 32, 01.07.2017

Yusuf Erdem Hasan Ogunmez Huseyin Budak

https://izlik.org/JA27MR23YP

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

• H. Angulo, J. Gimenez, A. M. Moros, and K. Nikodem, On strongly h-convex function, Ann. Funct. Anal. 2(2), 2011, 85–91.
• 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.
• M. V. Cortez, Relative strongly h-convex functions and integral inequalities, Appl. Math. Inf. Sci. Lett. 4, No. 2, 1-7 (2016).
• S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
• 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.
• H. Hudzik, L. Maligranda, Some remarks on s-convex functions. Aequ. Math. 48, 100-111 (1994).
• M. E. Kiris and M. Z. Sarikaya, Some generalized inequalities for Hermite-Hadamard’s integral inequalities and applications, submited (2015).
• J. Makó and A. Házy, On strongly convex functions. Carpathian Journal of Mathematics, 32 (1). 87-95.
• N. Merentes, K. Nikodem, Remarks on strongly convex functions, Aequationes Math. 80 (2010) 193–199.
• K. Nikodem, Z. Pales, Characterizations of inner product spaces be strongly convex functions, Banach J. Math. Anal. 5 (2011) 83–87.
• 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.
• J.E. Pečarić, F. Proschan and Y.L. Tong, Convex functions, partial orderings and statistical applications, Academic Press, Boston, 1992.
• B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restictions, Soviet Math. Dokl. 7 (1966), 72–75.
• 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.
• M. Z. Sarikaya, On strongly φ_h-convex functions in inner product spaces, Arabian Journal of Mathematics, (2013) 2:295–302.
• 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.
• 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.
• 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).
• 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.
• M. Z. Sarikaya, On Hermite Hadamard-type inequalities for strongly φ-convex functions, Southeast Asian Bull. Math., 39(1) (2015) , pp: 123-132.
• 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.