Simpson Type Inequalities Research Articles

Some Hadamard and Simpson type inequalities via s-convexity and their applications

Abstract In this study, the authors establish and generalize some inequalities of Hadamard and Simpson type based on s-convexity in the second sense. Some applications are also given and generalized. Examples are given to show the results. The results generalize the integral inequalities in articles of Sarikaya and Xi.

Generalized Simpson type inequalities involving Riemann-Liouville fractional integrals and their applications

We establish a Simpson type identity and several Simpson type inequalities for Riemann-Liouville fractional integrals. As applications, we apply the obtained results to special means of real numbers, an error estimate for Simpson type quadrature formula, and q-digamma function, respectively.

Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions

In this paper, we present a new definition of higher-order generalized strongly preinvex functions. Moreover, it is observed that the new class of higher-order generalized strongly preinvex functions characterize various new classes as special cases. We acquire a new q 1 q 2 -integral identity, then employing this identity, we establish several two-variable q 1 q 2 -integral inequalities of Simpson-type within a class of higher-order generalized strongly preinvex and quasi-preinvex functions. Finally, the utilities of our numerical approximations have concrete applications.

Some inequalities of Hermite–Hadamard, Ostrowski and Simpson type for (ξ,m,MT)-preinvex functions

In this paper, we first introduce a new class of [Formula: see text]-preinvex functions, which are called [Formula: see text]-preinvex functions, then we give some new estimates of Hermite–Hadamard, Ostrowski and Simpson type inequalities using Riemann–Liouville fractional integral. The obtained results in this paper generalize the well-known results in recent years.

CERTAIN INTEGRAL INEQUALITIES CONSIDERING GENERALIZED m-CONVEXITY ON FRACTAL SETS AND THEIR APPLICATIONS

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.

Estimation-type results on the k-fractional Simpson-type integral inequalities and applications

ABSTRACTWe 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.

Quantum Integral Inequalities of Simpson-Type for Strongly Preinvex Functions

In this paper, we establish a new q-integral identity, the result is then used to derive two q-integral inequalities of Simpson-type involving strongly preinvex functions. Some special cases of the obtained results are also considered, it is shown that several new and previously known results can be derived via generalized strongly preinvex functions and quantum integrals.

Some integral inequalities for multiplicatively geometrically P-functions

In this manuscript, by using a general identity for differentiable functions we can obtain new estimates on a generalization of Hadamard, Ostrowski and Simpson type inequalities for functions whose derivatives in absolute value at certain power are multiplicatively geometrically P-functions. Some applications to special means of real numbers are also given.

More results on integral inequalities for strongly generalized ( phi,h,s )-preinvex functions

The main goal of this research is to introduce a new form of generalized Hermite–Hadamard and Simpson type inequalities utilizing Riemann–Liouville fractional integral by a new class of preinvex functions which is known as strongly generalized ( phi,h,s )-preinvex functions in the second sense. It is observed that the derived inequalities are generalizations of the inequalities obtained by W. Liu, W. Wen (Filomat 30(2):333–342, 2016).

Generalization of different type integral inequalities for generalized (𝑠, 𝑚)-preinvex Godunova–Levin functions

Abstract In the present paper, the notion of generalized ( s , m ) {(s,m)} -preinvex Godunova–Levin function of second kind is introduced, and some new integral inequalities involving generalized ( s , m ) {(s,m)} -preinvex Godunova–Levin functions of second kind along with beta function are given. By using a new identity for fractional integrals, some new estimates on generalizations of Hermite–Hadamard, Ostrowski and Simpson type inequalities for generalized ( s , m ) {(s,m)} -preinvex Godunova–Levin functions of second kind via Riemann–Liouville fractional integral are established.

On generalization of some inequalities for generalized harmonically convex functions via local fractional integrals

Based on the theory of local fractional calculus and generalized harmonically convex function on fractal sets, the author establishes a general identity involving local fractional integrals. Using this identity, some inequalities on generalization of Hermite-Hadamard, Ostrowski and Simpson type inequalities for functions whose absolute values of derivatives are generalized harmonically convex function involving local fractional integrals are obtained. Finally, some applications of these inequalities for α-type special means are given.

Some different type integral inequalities concerning twice differentiable generalized relative semi-$(r; m, h)$-preinvex mappings

In this article, we first present some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-$(r; m, h)$-preinvex mappings. And then, a new identity concerning twice differentiable mappings defined on $m$-invex set is derived. By using the notion of generalized relative semi-$(r; m, h)$-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard, Ostrowski and Simpson type inequalities via fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

Some new simpson type inequalities for the p-convex and p-concave functions

In this paper, we establish some new Simpson type inequalities for the class of functions whose derivatives in absolute values at certain powers are p-convex and p-concav

Weighted Simpson type inequalities for h-convex functions

Weighted Simpson type inequalities for h-convex functions

Ostrowski and Simpson Type Inequalities for Strongly Reciprocally Convex Functions

Ostrowski and Simpson Type Inequalities for Strongly Reciprocally Convex Functions

Simpson type integral inequalities for convex functions via Riemann-Liouville integrals

In this paper some new inequalities of Simpson-type are established for the classes of functions whose derivatives of absolute values are convex functions via Riemann-Liouville integrals. Also, by special selections of n, we give some reduced results.

Integral inequalities for differentiable p-harmonic convex functions

In this paper, we consider a new class of harmonic convex functions, which is called p-harmonic convex function. Several new Hermite-Hadamard, midpoint, Trapezoidal and Simpson type inequalities for functions whose derivatives in absolute value are p-harmonic convex are obtained. Some special cases are discussed. The ideas and techniques of this paper may stimulate further research.

A generalization of Simpson’s inequality via differentiable mapping using extended (s, m)-convex functions

The authors deduce a differentiable mapping integral identity with two parameters. Using this integral identity, this paper establishes new inequalities of Simpson type for extended (s, m)-convex functions under certain conditions. This contributes to new better estimates than the earlier results. Finally, these inequalities are applied to special means.

On the Generalization of Simpson Type Inequalities for Quasi-convex Functions

In this paper, we establish the generalization of inequalities of the Simpson type for functions whose absolute values of derivatives are quasi-convex.

More results on Simpson's type inequality through convexity for twice differentiable continuous mappings.

Our aim in this article is to incorporate the notion of “strongly s-convex function” and prove a new integral identity. Some new inequalities of Simpson type for strongly s-convex function utilizing integral identity and Holder’s inequality are considered.