ON SOME NEW INEQUALITIES FOR s-CONVEX FUNCTIONS

Year 2019, Volume: 9 Issue: 1, 101 - 113, 01.03.2019

Mehmet Eyup Kırıs Hasan Kara

Abstract

In this paper, we establish a few new generalization of Hermite-Hadamard inequality using s-convex functions in the 2nd sense. For this purpose we used some special inequalities like Holder's.

Keywords

Convex Function, s-Convex Functions, Holder Inequality, Hermite-Hadamrd Inequality

References

• [1] Cristescu G., (2004), Hadamard Type Inequalities for ϕ - Convex Functions, Annals of the University of Oradea, Fascicle of Management and Technological Engineering, CD-Rom Edition, III(XIII).
• [2] Noor, M.A., Noor, K.I., Awan, M.U., (2014), Hermite-Hadamard inequalities for relative semi-convex functions and applications, Filomat, 28, no. 2,51-55.
• [3] Kırmacı U.S., (2004), Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp., 147, 137-146
• [4] Dragomir S. S. and Agarwal R.P., (1998), Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (5), 91-95.
• [5] Bakula M. K. and Peˇcari´c J., (2004), Note on some Hadamard-type inequalities, Journal of Inequalities in Pure and Applied Mathematics, vol. 5, no. 3, article 74.
• [6] Set E., Ozdemir M. E., and Dragomir S. S., (2010), ¨ On Hadamard-Type inequalities involving several kinds of convexity, Journal of Inequalities and Applications, Article ID 286845, 12 pages.
• [7] Cristescu G. and Lup¸sa L., (2002), Non-connected convexities and applications, Kluwer Academic Publishers, Dordrecht / Boston / London.
• [8] Dragomir S.S. and Fitzpatrick S., (1999), The Hadamard’S inequality for s-convex functions in the second sense. Demonstratio Mathematica, 32(4): 687-696
• [9] Dragomir S. S. and Pearce C. E. M., (2000), Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University.
• [10] Dragomir S. S., Peˇcari´c J. and Persson L. E., (1995), Some inequalities of Hadamard type, Soochow J. Math. 21, 335-241.
• [11] Peˇcari´c J.E., Proschan F. and Tong Y.L., (1992), Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston.
• [12] Pearce C.E.M. and Peˇcari´c J., (2000), Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett., 13(2), 51–55.
• [13] Youness E. A., (1999), E - Convex Sets, E - Convex Functions and E - Convex Programming, Journal of Optimization Theory and Applications, 102, 2, 439-450.
• [14] Sarikaya M. Z., (2013), On Hermite Hadamard-type inequalities for strongly ϕ-convex functions, Southeast Asian Bull. Math., in press.
• [15] Sarikaya M. Z., (2014), On Hermite Hadamard-type inequalities for ϕh-convex functions, Kochi J. of Math., 9, 83-90.
• [16] Sarikaya M.Z.,Buyukeken M., Kiris M.E., (2015), On some generilazed integral inequalities for ϕconvex functions, Stud.Univ. Babes-Bolyai Math. 60, No. 3, 367-377.
• [17] Hudzik H., Maligranda L., (1994), Some remarks on s-convex functions, Aequationes Math, 48 : 100-111.
• [18] Tseng, K., Hwang, S. & Dragomir, S. (2017). On Some New Inequalities of Hetmite-Hadamard-Fejer Type Involving Convex Functions, Demonstratio Mathematica, 40(1), pp. 51-64. Retrieved 28 Apr. 2018, from doi:10.1515/dema-2007-0108
• [19] Kirmaci U.S., Bakula M.K., Ozdemir M.E, Pecaric J., (2007), Applied Mathematics and Computation, 193 26–35.
• [20] Pachpatte, B. G., (1992). On Some Inequalities for Convex Functions, RGMIA Res. Rep. Coll.6, suplement.
• [21] Sarikaya MZ, Set E, Ozdemir ME., 2010, ¨ On new inequalities of Simpson’s type for s -convex functions. Comput. Math. Appl. ,60: 2191–2199. 10.1016/j.camwa.2010.07.033.
• [22] Ozdemir, M.E., Latif, M.A. and Akdemir, A.O., (2012), On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates, Journal of Inequalities and Applications ,DOI: 10.1186/1029-242X-2012-21.
• [23] Hussain, S., Bhatti, M.I. and Iqbal, M., (2009), Hadamard-type inequalities for s-convex functions I, Punjab Univ. J. Math., 41 pp. 51-60.
• [24] Ozdemir, M.E., Kavurmacı, H., Akdemir A.O. and Avcı, M., (2012), Inequalities for convex and sconvex functions on 4 = [a, b] × [c, d], Journal of Inequalities and Applications, February, 2012:20, doi:10.1186/1029-242X-2012-20.
• [25] Alomari, M., Darus, M., Dragomir, S.S., (2009), New inequalities of Simpsons type for s-convex functions with applications, RGMIA Res. Rep. Coll., 12 (4) Article 9. Online http://ajmaa.org/RGMIA/v12n4.php.
• [26] Akdemir, A.O., Ozdemir, M.E., Varosanec, S., (2012), On some inequalities for h-concave functions, Mathematical and Computer Modelling , ”55-(3-4)”, 746-753 pp., DOI: 10.1016/j.mcm.2011.08.051.
• [27] Ozdemir, M.E., Yıldız, Y., Akdemir, A.O. and Set, E., (2013), On some inequalities for s-convex functions and applications, Journal of Inequalities and Applications , DOI: 10.1186/1029-242X-2013- 333.
• [28] Akdemir, A.O., Avcı-Ardı¸c, M. and Ozdemir, M.E., (2017), Inequalities via s-convexity and log – convexity, Topological Algebra and Its Applications, 5:74–85.