Some new general integral inequalities for $P$-functions

Imdat ISCANa, Erhan SETb and M. Emin OZDEMIRc

Some new general integral inequalities for $P$-functions

Authors :

Imdat ISCAN^a, Erhan SET^b and M. Emin OZDEMIR^c

Author Address :

aDepartment of Mathematics, Faculty of Arts and Sciences, Giresun University, 28100, Giresun, Turkey.
bDepartment of Mathematics, Faculty of Arts and Sciences, Ordu University, 52200, Ordu, Turkey.
aAtat¨urk University, K.K. Education Faculty, Department of Mathematics, 25240, Campus, Erzurum, Turkey.

Abstract :

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are $P$-functions. Some applications to special means of real numbers are also given.

Keywords :

Convex function, $P$-function, Simpson’s inequality, Hermite-Hadamard’s inequality.

DOI :

Article Info :

Received : April 25, 2014; Accepted : July 31, 2014.