On some Hermite-Hadamard type inequalities for strongly s-convex functions

Year 2017, Volume: 5 Issue: 3, 154 - 161, 01.07.2017

Yusuf Erdem , Hasan Ogunmez Huseyin Budak

https://izlik.org/JA59XL58EL

Abstract

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

Keywords

Hermite-Hadamard type inequalities , Hölder inequality , strongly s-convex functions

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. Pecaric, Note on some Hadamard-type inequalities, Journal of Inequalities in Pure and Applied Mathematics, vol. 5, no. 3, article 74, 2004.
• 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).
• J. Mako and A. Hazy, 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, C¸ . 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. Pecaric, 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, On strongly jh−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 ofMathematics, 1(2), 33-40 (2013)
• M. Z. Sarikaya and K. Ozcelik, On Hermite-Hadamard type integral inequalities for strongly jh−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 j-convex functions, Southeast Asian Bull. Math., 39(1) (2015) , pp: 123-132.