Abstract
In this study, by using a new identity we establish some new Simpson type inequalities for differentiables–convex functions in the second sense. Various special cases have been studied in details. Also, in order to illustrate the efficient of our main results, some applications to special means and weighted Simpson quadrature formula are given. The obtained results generalize and refine certain known results. At the end, a brief conclusion is given as well.
Highlights
Definition 1.1. ([1]) Let I be an interval of real numbers
Various special cases have been studied in details
The concept of convex functions has been generalized in diverse manners
Summary
Definition 1.1. ([1]) Let I be an interval of real numbers. A function ψ : I → R is said to be convex, if for all λ1, λ2 ∈ I and all χ ∈ [0, 1], we have ψ (χλ1 + (1 − χ) λ2) χψ (λ1) + (1 − χ) ψ(λ2). In [10], Alomari et al established the following Simpson type inequalities for s-convex functions. If |ψ | is s–convex on [λ1, λ2] for some fixed s ∈ In [11], Sarikaya et al gave the following results Simpson type inequalities for differentiable convex functions. If |ψ |qis convex on [λ1, λ2], q 1, the following inequality holds: 51−. In this paper, inspired by the above mentioned studies, we will establish a new identity and applying it to derive new weighted Simpson type inequalities for s– convex functions in the second sense. A brief conclusion will be provided as well
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