Abstract
In this study, we introduced new integral inequalities of Hermite–Hadamard type via s-convexity and studied their properties. The absolute form of the first and second derivatives for the new inequalities is considered to be s-convex. As an application, the inequalities were applied to the special means of real numbers. We give the error estimates for the midpoint formula.
Highlights
1 Introduction Due to the significant roles played by convex functions, they exist in many fields of studies including life and management sciences, engineering and optimization [1, 2]
Many existing inequalities, reported in the literature, emerged from convex functions [3,4,5]. One of such fundamental inequalities that have been widely reported in the literature is of the Hermite–Hadamard type
The two inequalities for differentiable convex mapping of Hadamard type were introduced by Dragomir and Agarwal [9]; the results can be proved by applying the following lemma
Summary
Due to the significant roles played by convex functions, they exist in many fields of studies including life and management sciences, engineering and optimization [1, 2]. Given the generalization of inequalities, Dragomir and Fitzpatrick studied a Hermite– Hadamard type in the second sense for an s-convex function [3]. Theorem 1 Let ψ : [0, ∞) → [0, ∞) be an s-convex function in the second sense, whereby s ∈ (0, 1], and u, v ∈ [0, ∞), u < v. The two inequalities for differentiable convex mapping of Hadamard type were introduced by Dragomir and Agarwal [9]; the results can be proved by applying the following lemma.
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