On some inequalities of Hermite-Hadamard type via m-convexity

Abstract In this paper we give some estimates to the right-hand side of Hermite–Hadamard inequality for functions whose absolute values of second derivatives raised to positive real powers are m -convex.

[1]  E. Beckenbach.  CONVEX FUNCTIONS , 2007 .

[2]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[3]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[4]  S. Dragomir,et al.  Some remarks on the trape-zoid rule in numerical integration , 1999 .

[5]  D. S. Mitrinovic,et al.  Classical and New Inequalities in Analysis , 1992 .

[6]  S. Dragomir.  Two Mappings in Connection to Hadamard's Inequalities , 1992 .

[7]  C. E. M. Pearce,et al.  Inequalities for differentiable mappings with application to special means and quadrature formulæ , 2000, Appl. Math. Lett..

[8]  Y. Tong,et al.  Convex Functions, Partial Orderings, and Statistical Applications , 1992 .

[9]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[10]  M. KLARI,et al.  COMPANION INEQUALITIES TO JENSEN’S INEQUALITY FOR m-CONVEX AND (α, m)-CONVEX FUNCTIONS , 2006 .

[11]  M. Emin Ozdemir,et al.  Hadamard Type Inequalities for m-Convex and ({\alpha},m)-Convex Functions via Fractional Integrals , 2012 .

[12]  Ugur S. Kirmaci,et al.  Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula , 2004, Appl. Math. Comput..

[13]  Maslina Darus,et al.  Inequalities of Hermite-Hadamard's Type for Functions Whose Derivatives Absolute Values are Quasi-Convex , 2009 .

[14]  J. Pečarić,et al.  HADAMARD TYPE INEQUALITIES FOR M-CONVEX AND (ALPHA, M)-CONVEX FUNCTIONS , 2008 .

[15]  M. Emin Özdemir,et al.  On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula , 2004, Appl. Math. Comput..