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

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.2010 Mathematics subject classification: primary 26A51; secondary 26D15.

Hermite-Hadamard and Simpson Type Inequalities for Differentiable P-GA-Functions

“…In recent years, many authors have studied errors estimations for Hermite-Hadamard and Simpson inequalities; for refinements, counterparts, and generalization concerningfunctions and GA-convex, see [4][5][6][7][8][9][10][11].…”

“…Theorem 2. Let : [ , ] → R be a four times continuously differentiable mapping on ( , ) and ‖ (4) ‖ ∞ = sup ∈( , ) | (4) ( )| < ∞. Then the following inequality holds:…”

Integral inequalities under beta function and preinvex type functions

“…The function , where is said to be P -convex on a convex set, if for every and For the applications of P -convex function and its generalizations, we refer Akdemir and Ozdemir ( 2010 ), Barani and Barani ( 2012 ), Liu ( 2013 , 2014 ), Tunc ( 2013 ) and Varosanec ( 2007 ).…”

Hermite-Hadamard Inequality for Geometrically Quasiconvex Functions on a Rectangular Box

“…is known in the literature as Hermite-Hadamard inequality for convex functions (see for example [5]). In resent years there have been many extensions, generalizations, refinements and similar results of Hetmite-Hadamard inequality, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and references therein.…”