Abstract
In the paper, the authors establish some new inequalities of Hermite-Hadamard type for functions whose third derivatives are convex. MSC: 26D15, 26A51, 41A55.
Highlights
It is common knowledge in mathematical analysis that a function f : I ⊆ R → R is said to be convex on an interval I if the inequality f λx + ( – λ)y ≤ λf (x) + ( – λ)f (y) ( . )is valid for all x, y ∈ I and λ ∈ [, ]
In the paper, the authors establish some new inequalities of Hermite-Hadamard type for functions whose third derivatives are convex
Theorem . ([, Theorem ]) Let f : I ⊆ R → R be differentiable on I◦ such that f ∈ L([a, b]) and a, b ∈ I◦ with a < b
Summary
Abstract In the paper, the authors establish some new inequalities of Hermite-Hadamard type for functions whose third derivatives are convex. Introduction It is common knowledge in mathematical analysis that a function f : I ⊆ R → R is said to be convex on an interval I if the inequality f λx + ( – λ)y ≤ λf (x) + ( – λ)f (y) is valid for all x, y ∈ I and λ ∈ [ , ]. If f : I ⊆ R → R is a convex function on I and a, b ∈ I with a < b, the double inequality f a + b ≤ b f (x) dx ≤ f (a) + f (b) holds.
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