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

Abstract

In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi
$$\underset{a}{\stackrel{a+\eta (b,a)}{\int }}{(x-a)}^p{(a+\eta (b,a)-x)}^{q}f\left(x\right)dx$$
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