SOME NEW HERMITE-HADAMARD TYPE FRACTIONAL INTEGRAL INEQUALITIES TO PRODUCTS OF TWO GENERALIZED (r; g, s,m,\phi)-PREINVEX FUNCTIONS

Artion Kashuri
2018 Matematicki bilten  
In the present paper, a new class of generalized (r; g, s, m, ϕ)preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving products of two generalized (r; g, s, m, ϕ)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities to products of two generalized (r; g, s, m, ϕ)-preinvex functions via Riemann-Liouville fractional integrals are established. These general
more » ... general inequalities give us some new estimates for the left-hand side of Gauss-Jacobi type quadrature formula and Hermite-Hadamard type fractional integral inequalities and also extend some results appeared in the literature (see [1] ). Some conclusions and future research are also given. 2000 Mathematics Subject Classification. Primary: 26A51. Secondary: 26A33, 26D07, 26D10, 26D15. Key words and phrases. Hermite-Hadamard type inequality, Hölder's inequality, Minkowski's inequality, Cauchy's inequality, power mean inequality, Riemann-Liouville fractional integral, s-convex function in the second sense, m-invex, P -function. 75
doi:10.37560/matbil18100075k fatcat:4kvc7u7jh5a4fgt7ot3mqfoqty