Fractional Hermite-Hadamard type inequalities for subadditive functions

Abstract

In this paper, we establish different variants of fractional Hermite-Hadamard inequalities for subadditive functions via Riemann-Liouville fractional integrals. Moreover, we offer some fractional integral inequalities for the product of two subadditive functions via Riemann-Liouville fractional integrals. It is also shown that the inequalities offered in this research are the generalization of the already given inequalities for convex functions and subadditive functions.

Hermite-Hadamard Like Inequalities for Exponentially Subadditive Functions via Fractional Integrals

“…This inequality can be easily captured by using the Jensen's inequality for convex functions. For more recent findings concerning (1) reader can read [4,7,14]. Please refer also to [20,21,24].…”

“…If we use s = 0 in Theorem 2.2, then we have[1, Theorem 8 (2.7)]. If we take φ (δµ) ≤ δφ (µ) and s = 0 in Theorem 2.2, then we have[1, Corollary 2].…”

“…If we use s = 0 in Theorem 2.2, then we have[1, Theorem 8 (2.7)]. If we take φ (δµ) ≤ δφ (µ) and s = 0 in Theorem 2.2, then we have[1, Corollary 2]. Let φ, ϕ : I = [0, ∞) → R be two continuous exponentially subadditive functions, κ 1 , κ 2 ∈ I • with κ 1 < κ 2 .…”

“…1 (φ(1 − δ)κ 2 )(ϕ(1 − δ)κ 2 ) e 2s((1−δ)κ2) + φ(δκ 2 )ϕ(δκ 2 ) e 2sδκ2 dδ + δ α−1 φ(δκ 1 )ϕ((1 − δ)κ 2 ) e s(δκ1+(1−δ)κ2) + φ((1 − δ) κ 1 )ϕ(δκ 2 ) e s(δκ2+(1−δ)κ1) + δ α−1 (φ(1 − δ)κ 2 )ϕ(δκ 1 ) e s((1−δ)κ2+δκ1) + φ(δκ 2 )ϕ((1 − δ) κ 1 )e s((1−δ)κ1+δκ2) dδ.…”