Artion Kashuri, Rozana Liko, Some new integral inequalities for generalized $(s,m,\varphi)$-preinvex Godunova-Levin functions, Volume 2018, Number 1, Pages 134-145, 2018

# Artion Kashuri, Rozana Liko, Some new integral inequalities for generalized $(s,m,\varphi)$-preinvex Godunova-Levin functions, Volume 2018, Number 1, Pages 134-145, 2018

Abstract: In the present paper, a new class of generalized $(s,m,\varphi)$-preinvex Godunova-Levin function of the second kind is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula are given. Moreover, by using new identity via classical integrals some Hermite-Hadamard, Simpson and midpoint type inequalities for generalized $(s,m,\varphi)$-preinvex Godunova-Levin functions of the second kind are established.

Keywords: Hermite-Hadamard inequality, Simpson type inequality, midpoint inequality, H\"{o}lder's inequality, power mean inequality, $m$-invex, $P$-function.

Artion Kashuri, Rozana Liko, Some new integral inequalities for generalized $(s,m,\varphi)$-preinvex Godunova-Levin functions, International Journal of Advances in Mathematics, Volume 2018, Number 1, Pages 134-145, 2018.