International Journal of Advances in Mathematics
International Journal of Advances in Mathematics
2456-6098
Volume 2018
Number 1
2018
January
1
Some new integral inequalities for generalized $(s,m,\varphi)$-preinvex Godunova-Levin functions
134
145
EN
Artion
Kashuri
Department of Mathematics,
Faculty of Technical Science, University Ismail Qemali,
Vlora, Albania.
artionkashuri@gmail.com
Rozana
Liko
Department of Mathematics,
Faculty of Technical Science, University Ismail Qemali,
Vlora, Albania.
artionkashuri@gmail.com
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.
Hermite-Hadamard inequality, Simpson type inequality, midpoint inequality, H\"{o}lder's inequality, power mean inequality, $m$-invex, $P$-function.
http://adv-math.com/artion-kashuri-rozana-liko-new-integral-inequalities-generalized-smvarphi-preinvex-godunova-levin-functions-volume-2018-number-1-pages-134-145-2018/
http://adv-math.com/wp-content/uploads/2018/01/Article-accepted-2017-11-03.pdf