Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators

Abstract

Abstract:In this present work, the authors establish a new integral identity involving generalized fractional integral operators and by using this fractional-type integral identity, obtain some new Hermite-Hadamard type inequalities for functions whose rst derivatives in absolute value are convex. Relevant connections of the results presented here with those earlier ones are also pointed out.

Fractional Versions of Hadamard-Type Inequalities for Strongly Exponentially α , h − m -

“…e outcomes of this article give refinements and generalizations of fractional integral inequalities for different types of convex functions deducible from the definition of the exponentially (α, h − m)-convex function. [39][40][41].…”

General inequalities related Hermite-Hadamard inequality for generalized fractional integrals

“…For instance the classical Riemann-Liouville fractional integrals J α a+ and J α b− of order α follow easily by setting λ = α, σ(0) = 1 and w = 0 in (1.3) and (1.4). Also, to see more results and generalizations for convex and some other several convex functions classes, as Q(I), P (I), SX(h, I) and r−convex, involving generalized fractional integral operators, see [17,14,15,10,9,13,12,19,20] and references there in.…”