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We utilize the definition of a fractional integral operators, which was presented by Ahmad et al., to investigate a general fractional-type identity with a parameter. We establish certain parameterized fractional integral inequalities based on this identity, and provide two examples to illustrate the obtained results. Also, these results derived in this paper are applied to the estimations of q-digamma function, divergence measures and cumulative distribution function, respectively.

In this paper, the new version of the celebrated Montgomery identity is determined via quantum integral operators. By using it, certain quantum integral inequalities of Ostrowski type are established. Moreover, the relevant connection of the obtained results of this work with the derived results in previously published works is discussed.

We use the definition of a fractional integral operators, proposed by Katugampola, to establish a fractional Hermite-Hadamard's inequality for p-convex mappings and an identity with two parameters. We derive several parameterized integral inequalities associated with this identity, and provide three examples to illustrate the obtained results.

We establish a (p, q)-integral identity with parameters and certain new (p, q)-integral inequalities of different types through (p, q)-differentiable mappings. Many results obtained in this article provide significant extensions of other related results given in the literature. Furthermore, we construct three examples to illustrate the investigated results.

This paper aims to establish k-fractional integral inequalities with multiple parameters involving the first differentiable mappings. Applications of our results to random variables are also given.

We establish a Simpson-type identity of multiparameter and certain Simpson-type inequalities via k-fractional integrals. Worth mentioning, the obtained inequalities in this article generalize some results presented by Set et al. [Simpson type integral inequalities for convex functions via Riemann-Liouville integrals. Filomat. 2017;31(14):4415–4420] and Sarikaya et al. [On new inequalities of Simpson's type for s-convex functions. Comput Math Appl. 2010;60:2191–2199]. As applications, we also provide several inequalities for f-divergence measures and probability density functions. We expect that this study will be result in the new k-fractional integration explorations for Simpson-type inequalities.

In this paper, we first introduce the concept of generalized relative semi-(m,h)-preinvex functions, and then a new k-Riemann–Liouville fractional integral identity for differentiable mapping is de...

A $k$ -fractional integral identity with multiple parameters is investigated. Based on this identity, some estimation-type results related to $k$ -fractional integral inequalities for the first-order differentiable functions are obtained. These results are then applied to the estimation of cumulative distribution function and some other special means.

We investigate a weighted Simpson-type identity and obtain new estimation-type results related to the weighted Simpson-like type inequality for the first-order differentiable mappings. We also present some applications to f-divergence measures and to higher moments of continuous random variables.

We establish some interesting refinements of the $(p,q)$ ( p , q ) -Hölder integral inequality and the $(p,q)$ ( p , q ) -power-mean integral inequality. As applications, we show that some existing $(p,q)$ ( p , q ) -integral inequalities can be improved by the results obtained in this paper.

We establish a Hermite-Hadamard type identity and several new Hermite-Hadamard type inequalities for conformable fractional integrals and present their applications to special bivariate means.

In this article, we first presented a new integral identity concerning differentiable mappings defined on m-invex sets. By using the notion of generalized relative semi-(r; m, p, q, h1, h2)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Ostrowski type inequalities are established. It is pointed out that some new special cases can be deduced from main results of the article.

The purpose of this work is to investigate some inequalities for generalized [Formula: see text]-convexity on fractal sets [Formula: see text], which are associated with Simpson-like inequalities. To this end, an improved version of Hölder inequality and a Simpson-like identity on fractal sets are established, in view of which we give several estimation-type results involving Simpson-like inequalities for the first-order differentiable mappings. Moreover, we provide five examples to illustrate our results. As applications with respect to local fractional integrals, we derive two inequalities according to [Formula: see text]-type special means and generalized probability density functions.

The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

Using an integral identity for a once differentiable mapping, this paper es- tablishes Hadamard's integral inequalities for s-convex and s-concave mappings. In particular, our results improve and extend some known ones in the literature. Finally, these inequalities are applied to special means. AMS subject classifications: 26D15, 26A51, 26E60, 41A55

By using power-mean integral inequality and Holder’s integral inequality, this paper establishes some new inequalities of Simpson type for functions whose three derivatives in absolute value are the class of (α, m)-geometric-arithmetically-convex functions. Finally, some applications to special means of positive real numbers have also been presented.

This article aims to investigate certain inequalities for generalized h-convexity on fractal sets R α , which are related to the famous Fejer–Hermite–Hadamard inequality. For this purpose, two identities for local differentiable mappings are established, based on which we provide certain estimates for the difference between the left and middle part as well as that of the middle and right part in the Fejer–Hermite–Hadamard inequality. Furthermore, we present five examples to illustrate the obtained results. As applications related to local fractional integrals, we construct several inequalities for random variables, cumulative distribution functions and numerical integrations.

First, we introduce a generalized [Formula: see text]-convexity concept defined on the real linear fractal set [Formula: see text] [Formula: see text] and discuss the relation between generalized [Formula: see text]-convexity and [Formula: see text]-convexity. Second, we present several important properties of the generalized [Formula: see text]-convex mappings. Meanwhile, via local fractional integrals, we also derive certain estimation-type results on generalizations of Hadamard-type, Fejér-type and Simpson-type inequalities. As applications related to local fractional integrals, we construct several inequalities for generalized probability density mappings and [Formula: see text]-type special means.