On some generalized integral inequalities for φ-convex functions

Authors

  • Mehmet Zeki SARİKAYA Duzce University, Department of Mathematics Faculty of Science and Arts Duzce, Turkey e-mail: sarikayamz@gmail.com
  • Meltem BÜYÜKEKEN Düzce University, Department of Mathematics Faculty of Science and Arts Düzce, Turkey e-mail: meltembuyukeken@gmail.com
  • Mehmet Eyüp KIRIS Afyon Kocatepe University, Department of Mathematics Faculty of Science and Arts Afyon, Turkey e-mail: mkiris@gmail.com, kiris@aku.edu.tr

Keywords:

Hermite-Hadamard's inequality, convex function, φ-convex function, Hölder's inequality.

Abstract

The main goal of the paper is to state and prove some new general inequalities for φ-convex function.

Mathematics Subject Classification (2010): 26D15, 41A55, 26D10.

References

Cristescu, G., Lupsa, L., Non-connected convexities and applications, Kluwer Academic Publishers, Dordrecht/Boston/London, 2002.

Cristescu, G., Hadamard type inequalities for '-convex functions, Annals of the University of Oradea, Fascicle of Management and Technological Engineering, CD-Rom Edition, 12(2004), no. 3.

Bakula, M.K., Pecaric, J., Note on some Hadamard-type inequalities, Journal of Inequalities in Pure and Applied Mathematics, 5(2004), no. 3, article 74.

Dragomir, S.S., Pearce, C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.

Dragomir, S.S., Agarwal, R.P., 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.

Dragomir, S.S., Pecaric, J., Persson, L.E., Some inequalities of Hadamard type, Soochow J. Math., 21(1995), 335-241.

Kavurmaci, H., Avci, M., Ozdemir M.E., New inequalities of Hermite-Hadamard type for convex functions with applications, Journal of Inequalities and Applications, 2011, 2011:86.

Pecaric, J.E., Proschan, F., Tong, Y.L., Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.

Pearce, C.E.M., Pecaric, J., Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett., 13(2000), no. 2, 51-55.

Krmac, U.S., Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp., 147(2004), 137-146.

Noor, M.A., Noor, K.I., Awan, M.U., Hermite-Hadamard inequalities for relative semiconvex functions and applications, Filomat, 28(2014), no. 2, 221-230.

Ozdemir, M.E., Set, E., Alomari, M.W., Integral inequalities via several kinds of convexity, Creat. Math. Inform., 20(2011), no. 1, 62-73.

Ozdemir, M.E., Avc, M., Kavurmac_, H., Hermite-Hadamard-type inequalities via (α;m)-convexity, Comput. Math. Appl., 61(2011), 2614{2620.

Set, E., Ozdemir, M.E., Dragomir, S.S., On the Hermite-Hadamard inequality and other integral inequalities involving two functions, Journal of Inequalities and Applications, Article ID 148102, 9 pages, 2010.

Set, E., Ozdemir, M.E., Dragomir, S.S., On Hadamard-Type inequalities involving several kinds of convexity, Journal of Inequalities and Applications, Article ID 286845, 12 pages, 2010.

Youness, E.A., E-convex sets, E-convex functions and E-convex programming, Journal of Optimization Theory and Applications, 102(1999), no. 2, 439-450.

Sarikaya, M.Z., On Hermite Hadamard-type inequalities for strongly φ-convex functions, Southeast Asian Bull. Math. 2013, in press.

Sarikaya, M.Z., On Hermite Hadamard-type inequalities for φh-convex functions, Kochi J. of Math., 9(2014), 83-90.

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Published

2015-09-30

How to Cite

SARİKAYA, M. Z., BÜYÜKEKEN, M., & KIRIS, M. E. (2015). On some generalized integral inequalities for φ-convex functions. Studia Universitatis Babeș-Bolyai Mathematica, 60(3), 367–377. Retrieved from https://studia.reviste.ubbcluj.ro/index.php/subbmathematica/article/view/5771

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