INTEGRAL INEQUALITIES FOR SOME CONVEX FUNCTIONS

Year 2016, Volume: 2 Issue: 1, 1 - 6, 22.05.2016

Ahmet Ocak Akdemir , M. Emin Özdemir

Abstract

In this paper, we established some new integral inequalities for

different kinds of convex functions by using some classical inequalities.

Keywords

Convex functions, m convex functions, s convex log convex functions

References

• DRAGOMIR, S.S., (2002). On Some New Inequalities of Hermite-Hadamard Functions, Tamkang Journal of Mathematics, 33 (1). For 5 Convex
• BAKULA, M.K., PECARIC, J., RIBICIC, M., (2006). Companion inequalities to Jensen’s inequality for 5 convex and (<, 5) convex functions, J. Inequal. Pure Appl. Math., 7. Article 194.
• ÖZDEMIR, M.E., AVCI, M. and SET, E., (2010). On some inequalities of Hermite Hadamard type via 5 convexity, Appl. Math. Lett., 23 1065-1070. BAKULA, M.K., ÖZDEMİR, M.E. and PECARIC, J., (2008). Hadamard type inequalities for 5 convex and (<, 5) convex functions, J. Inequal. Pure Appl. Math., 9. Article 96. HUDZIK, H. and MALIGRANDA, L., (1994). Some remarks on
• convex functions, Aequationes
• Math., (48) 100-111.
• DRAGOMIR S.S. and TOADER, G., (1993). Some inequalities for University Babes Bolyai, Mathematica, 38 (1), 21- 28.
• TOADER, G., (1984). Some generalization of the convexity, Proc. Colloq. Approx. Opt., Cluj- Napoja, 329-338.
• TOADER, G., (1998). On a generalization of the convexity, Mathematica, 30 (53), 83-87.
• DRAGOMIR S.S., (2002). On some new inequalities of Hermite-Hadamard type for 5 convex functions, Tamkang Journal of Mathematics, 33 (1).
• BRECKNER, W.W., (1978). Stetingkeitsaussagen fur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearel Raumen, Pupl.Inst.Math., 23, 13-20.
• BRECKNER, W.W., (1993). Continuity of generalized convex and generalized concave set valued functions, Rev Anal., Number Thkor. Approx., 22, 39-51.
• DRAGOMIR, S.S. and FITZPATRICK, S., (1999). The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math., 32 (4), 687- 696.
• KIRMACI, U.S., BAKULA, M.K., ÖZDEMİR, M.E. and PECARIC, J., (2007). Hadamard-type inequalities for 8 convex functions, Applied Mathematics and Computation, 193, 26-35.
• ÖZDEMİR, M.E., SET, E. and SARIKAYA, M.Z., (2010). Konveks Fonksiyonlar Üzerine Notlar, Atatürk University.
• SARIKAYA, M.Z., SET, E. and ÖZDEMİR, M.E., (2011). Some new Hadamard’s type inequalits for co- ordinated functions, Hacettepe J. of. Math. and St., 40 219- 229.
• MIHEŞAN, V.G., (1993). Generalization of the convexity, Seminar of Functional Equations, Approx. and convex, Cluj-Napoca (Romania).
• SET, E., SARDARI, M., ÖZDEMIR, M.E. and ROOIN, J., (2009). On generalizations of the Hadamard inequality for (<, 5) convex functions, RGMIA Res. Rep. Coll., 12 (4), Article 4.
• ÖZDEMIR, M.E., KAVURMACI, H. and SET, E., (2010). Ostrowski’s type inequalities for (<, 5) convex functions, Kyungpook Math. J. 50, 371-378.
• ÖZDEMIR, M.E., AVCI, M. and KAVURMACI, H., (2011). Hermite-Hadamard- type inequalities via (<, 5) convextiy, Computers and Mathematics with Applications, 61, 2614-2620.
• PECARIC, J., PROSCHAN, F. and TONG, Y.L., (1992). Convex Statistical Applications, Acedemic Press, Inc. Orderings and