Abstract
An important area in the field of applied and pure mathematics is the integral inequality. As it is known, inequalities aim to develop different mathematical methods. Nowadays, we need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. The concept of convexity plays a strong role in the field of inequalities due to the behavior of its definition and its properties. Furthermore, there is a strong correlation between convexity and symmetry concepts. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the last few years. In this study, by using a new identity, we establish some new fractional weighted Ostrowski-type inequalities for differentiable quasi-convex functions. Further, further results for functions with a bounded first derivative are given. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtain. The obtained results generalize and refine certain known results.
Highlights
Computational and Fractional Analysis are nowadays more and more in the center of mathematics and of other related sciences either by themselves because of their rapid development, which is based on very old foundations, or because they cover a great variety of applications in the real world
Let φ be a differentiable function defined on the finite interval [a, b], whose derivative is integrable and bounded over [a, b], i.e., φ ∞ := supx∈(a, b)|φ (x)| < ∞, φ(x)
In order to illustrate the efficiency of our main results, some applications to special means will be obtain
Summary
Computational and Fractional Analysis are nowadays more and more in the center of mathematics and of other related sciences either by themselves because of their rapid development, which is based on very old foundations, or because they cover a great variety of applications in the real world. One of them is the quasi-convex function defined as follows: Definition 2 ([6]). Let φ be a differentiable function defined on the finite interval [a, b], whose derivative is integrable and bounded over [a, b], i.e., φ ∞ := supx∈(a, b)|φ (x)| < ∞, φ(x). In [22], Alomari et al gave the following midpoint type inequalities for differentiable quasi-convex. 1 q a Alomari and Darus in [23] obtained the Ostrowski-type inequalities for differentiable quasi-convex functions: Theorem 5 ([23]). If |φ |q is quasi-convex on [a, b], q ≥ 1, the following inequality holds:. We establish a new identity and apply it to derive new weighted Ostrowski-type inequalities for quasi-convex functions. In order to illustrate the efficiency of our main results, some applications to special means will be obtain
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