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Abstract
In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula.
Highlights
A real-valued function ψ : I ⊆ R → R is said to be convex on I if the inequality ψ θξ + ( – θ)ζ ≤ θψ(ξ ) + ( – θ)ψ(ζ ) ( . )holds for all ξ, ζ ∈ I and θ ∈ [, ]. ψ is said to be concave on I if inequality ( . ) is reversed
The improvements, generalizations, refinements and applications for the Hermite-Hadamard inequality have attracted the attention of many researchers [ – ]
5 Conclusion In this work, we find an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals, present some new inequalities for the arithmetic, logarithmic and generalized logarithmic means of two positive real numbers and provide the error estimations for the trapezoidal formula
Summary
A real-valued function ψ : I ⊆ R → R is said to be convex on I if the inequality ψ θξ + ( – θ)ζ ≤ θψ(ξ ) + ( – θ)ψ(ζ ) ( . )holds for all ξ , ζ ∈ I and θ ∈ [ , ]. ψ is said to be concave on I if inequality ( . ) is reversed. Let ψ : I ⊆ R → R be a convex function on the interval I, and c , c ∈ I with c < c .
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