Abstract
We consider the modified Hermite–Hadamard inequality and related results on integral inequalities, in the context of fractional calculus using the Riemann–Liouville fractional integrals. Our results generalize and modify some existing results. Finally, some applications to special means of real numbers are given. Moreover, some error estimates for the midpoint formula are pointed out.
Highlights
The generalization of certain integral inequalities to the fractional scope, in both continuous and discrete versions, have attracted many researchers in the recent few years and before [1, 19, 20]
Our work is devoted to Hadamard–Hermite type for convex functions in the framework of Riemann–Liouville fractional type integrals
For convex functions (1), many equalities and inequalities have been established by many authors; such as the Hardy type inequality [3], Ostrowski type inequality [7], Olsen type inequality [8], Gagliardo–Nirenberg type inequality [22], midpoint type inequality [10] and trapezoidal type inequality [14]
Summary
The generalization of certain integral inequalities to the fractional scope, in both continuous and discrete versions, have attracted many researchers in the recent few years and before [1, 19, 20]. A function g : I ⊆ R → R is said to be convex on the interval I, if the inequality g x + (1 – )y ≤ g(x) + (1 – )g(y) holds for all x, y ∈ I and ∈ [0, 1]. V–u u where g : I ⊆ R → R is assumed to be a convex function on I where u, v ∈ I with u < v. Hadamard inequality (2) for different classes of convex functions and mappings.
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