Integral Inequalities for Different Kinds of Convexity via Classical Inequalities

Year 2020, Volume: 5 Issue: 3, 305 - 313, 30.12.2020

Alper Ekinci , Ahmet Ocak Akdemir , Muhamet Emin Özdemir

Abstract

In this study, we obtain some new integral inequalities for different classes of convex functions by using classical inequalities like general Cauchy inequality and reverse Minkowski inequality.

Keywords

convex functions, m-convex functions, s-convex functions, Minkowski Inequality, (α,m)-convex functions

References

• M.K. Bakula, M.E. Özdemir and J. Peµcaric, Hadamard-type inequalities for m-convex and (α; m)convex functions, J. Inequal. Pure and Appl. Math., 9, (4), (2007), Article 96.
• M.K. Bakula, J. Peµcaric and M. Ribibic, Companion inequalities to Jensen's inequality for m-convex and (α; m)convex functions, J. Inequal. Pure and Appl. Math., 7 (5) (2006), Article 194.
• S.S. Dragomir and G. Toader, Some inequalities for mconvex functions, Studia University Babes Bolyai, Mathematica, 38 (1) (1993), 21-28.
• V.G. Mihe¸san, A generalization of the convexity, Seminar of Functional Equations, Approx. and Convex, Cluj-Napoca (Romania) (1993).
• G. Toader, Some generalization of the convexity, Proc. Colloq. Approx. Opt., Cluj-Napoca, (1984), 329-338.
• E. Set, M. Sardari, M.E. Ozdemir and J. Rooin, On generalizations of the Hadamard inequality for (α; m)convex functions, RGMIA Res. Rep. Coll., 12 (4) (2009), Article 4.
• M.E. Özdemir, M. Avcı and E. Set, On some inequalities of Hermite-Hadamard type via m-convexity, Applied Mathematics
• G. Toader, On a generalization of the convexity, Mathematica, 30 (53) (1988), 83-87.
• S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for mconvex functions, Tamkang Journal of Mathematics, 33 (1) (2002).
• H. Hudzik and L. Maligranda, Some remarks on sconvex functions, Aequationes Math., 48 (1994) 100-111.
• W.W. Breckner, Stetigkeitsaussagen fur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., 23 (1978) 13-20.
• W.W. Breckner, Continuity of generalized convex and generalized concave set-valued functions, Rev Anal. Number. Theor. Approx., 22 (1993) 39-51.
• S. Hussain, M.I. Bhatti and M. Iqbal, Hadamard-type inequalities for sconvex functions, Punjab University, Journal of Mathematics, 41 (2009) 51-60.
• S.S. Dragomir and S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the second sense, Demonstratio Math., 32 (4) (1999) 687-696.
• U.S. Kırmacı, M.K. Bakula, M.E. Özdemir and J. Peµcaric, Hadamard-type inequalities for s-convex functions, Applied Mathematics and Computation, 193 (2007) 26-35.
• L. Bougofa, On Minkowski and Hardy integral inequalities, Journal of Inequalities in Pure and Applied Mathematics, vol. 7, no. 2, article 60, 2006.
• Q.A. Ngo, D.D. Thang, T.T. Dat and D.A. Tuan, Notes on an integral inequality, Journal of Inequalities in Pure and Applied Mathematics, vol. 7, no. 4, article 120, 2