Rad HAZU, Matematičke znanosti, Vol. 22 (2018), 63-75.

HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (s,m,φ)-PREINVEX GODUNOVA-LEVIN FUNCTIONS

Artion Kashuri and Rozana Liko

Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", Vlora, Albania
e-mail: rozanaliko86@gmail.com

Abstract.   In the present paper, a new class of generalized (s,m,φ)-preinvex Godunova-Levin function of the second kind is introduced. Moreover, some left inequalities of Gauss-Jacobi type quadrature formula are given and some Hermite-Hadamard type inequalities for generalized (s,m,φ)-preinvex Godunova-Levin functions of the second kind via classical integrals are established. At the end, some applications to special means are given.

2010 Mathematics Subject Classification.   26A51, 26A33, 26D07, 26D10, 26D15.

Key words and phrases.   (s,m)-Godunova-Levin function, Hölder’s inequality, power mean inequality, m-invex, P-function.

DOI: https://doi.org/10.21857/m16wjc6rl9

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