Bulletin of the Australian Mathematical Society

Research Article

HERMITE–HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHEN A POWER OF THE ABSOLUTE VALUE OF THE FIRST DERIVATIVE IS P-CONVEX

A. BARANIa1 c1 and S. BARANIa2

a1 Department of Mathematics, Lorestan University, PO Box 465, Khoramabad, Iran (email: alibarani2000@yahoo.com, barani.a@lu.ac.ir)

a2 Department of Civil Engineering, Shahid Chamran University, PO Box 135, Ahvaz, Iran (email: seebb86@yahoo.com)

Abstract

In this paper we extend some estimates of the right-hand side of a Hermite–Hadamard type inequality for functions whose derivatives’ absolute values are P-convex. Applications to the trapezoidal formula and special means are introduced.

(Received August 31 2011)

2010 Mathematics subject classification

  • primary 26A51; secondary 26D15

Keywords and phrases

  • Hermite–Hadamard inequality;
  • P-convex;
  • trapezoidal formula;
  • special means

Correspondence:

c1 For correspondence; e-mail: alibarani2000@yahoo.com