New integral inequalities for $s$-preinvex functions

Meftah, Badreddine

doi:10.22075/ijnaa.2017.3084.1498

New integral inequalities for $s$-preinvex functions

Document Type : Research Paper

Author

Badreddine Meftah

Laboratoire des t\'{e}l\'{e}communications, Facult\'{e} des Sciences et de la Technologie, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria

10.22075/ijnaa.2017.3084.1498

Abstract

In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi
$$\underset{a}{\overset{a+\eta \left( b,a\right) }{\int }}\left( x-a\right)^{p}\left( a+\eta \left( b,a\right) -x\right) ^{q}f\left( x\right) dx$$
in the cases where $f$ and $\left| f\right| ^{\lambda }$ for $\lambda >1$, are $s$-preinvex functions in the second sense.

Keywords

Integral inequality

$s$-preinvex function

H"{o}lder inequality

power mean inequality