Abstract

We prove new Hermite-Hadamard inequalities for conformable fractional integrals by using convex function, s-convex, and coordinate convex functions. We prove new Montgomery identity and by using this identity we obtain generalized Hermite-Hadamard type inequalities.

Highlights

  • The class of convex functions is well known in the literature and is usually defined in the following way: let I be an interval in R; a function f : I → R is said to be convex on I if the inequality f (λx + (1 − λ) y) ≤ λf (x) + (1 − λ) f (y) (1)holds for all x, y ∈ I and λ ∈ [0, 1]

  • We prove new Hermite-Hadamard inequalities for conformable fractional integrals by using convex function, s-convex, and coordinate convex functions

  • In the paper [1], Hudzik and Maligranda considered a generalization of convex function, which is known as s-convex function in the second sense

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Summary

Introduction

The class of convex functions is well known in the literature and is usually defined in the following way: let I be an interval in R; a function f : I → R is said to be convex on I if the inequality f (λx + (1 − λ) y) ≤ λf (x) + (1 − λ) f (y) (1). Both inequalities hold in reverse direction if the function f is concave on the interval I This remarkable result was given in ([3], 1893) and is well known in the literature as Hermite-Hadamard inequality. Anderson [21] investigated the following conformable integral version of Hermite-Hadamard inequality. We prove new Hermite-Hadamard inequalities for conformable fractional integrals by using convex function, s-convex, and coordinate convex functions. We prove new Montgomery identity for conformable fractional integral By using this identity, we obtain Hermite-Hadamard type inequalities.

Hermite-Hadamard Inequalities
Generalization of Hermite-Hadamard Type Inequalities
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