Midpoint Inequalities Research Articles

On the Generalization of Some Hermite–Hadamard Inequalities for Functions with Convex Absolute Values of the Second Derivatives Via Fractional Integrals

We provide a unified approach to getting Hermite–Hadamard inequalities for functions with convex absolute values of the second derivatives via the Riemann–Liouville integrals. Some particular inequalities generalizing the classical results, such as the trapezoid inequality, Simpson’s inequality, and midpoint inequality are also presented.

Hermite-Hadamard's inequalities for conformable fractional integrals

In this paper, we establish the Hermite-Hadamard type inequalities forconformable fractional integral and we will investigate some integralinequalities connected with the left and right-hand side of theHermite-Hadamard type inequalities for conformable fractional integral. Theresults presented here would provide generalizations of those given inearlier works and we show that some of our results are better than the otherresults with respect to midpoint inequalities.

Fractional Ostrowski type inequalities for functions whose derivatives are s-preinvex

In this paper, some new fractional Ostrowski's inequalities for functions whose first derivatives in absolute value are $MT$-preinvex are established, mid point inequalities are also derived.

Generalization of Ostrowski inequality for convex functions

Abstract In this paper we establish some related Ostrowski inequalities for the case of convex functions and general Lebesgue integral on measurable spaces. Midpoint and integral mean inequalities are provided, some particular results related to the famous Fejér’s inequality are also given.

Ostrowski type inequalities for functions whose derivatives are h-convex in absolute value

Some new inequalities of Ostrowski type for functions whose derivatives are h-convex in modulus are given. Applications for midpoint inequalities are provided.

A GENERALIZATION OF OSTROWSKI TYPE INEQUALITY FOR MAPPINGS WHOSE SECOND DERIVATIVES BELONG TO L1(a,b) AND APPLICATIONS

In this paper, we will improve and generalize inequality of Os- trowski type for mappings whose second derivatives belong to L1 (a,b). Some well known inequalities can be derived as special cases. In addition, per- turbed mid-point inequality and perturbed trapezoid inequality are also ob- tained. The obtained inequalities have immediate applications in numerical integration where new estimates are obtained for the remainder term of the trapezoid and midpoint formula. Applications to some special means are also investigated.

A Unified Generalization of Perturbed Mid-Point and Trapezoid Inequalities and Asymptotic Expressions for Its Error Term

A Unified Generalization of Perturbed Mid-Point and Trapezoid Inequalities and Asymptotic Expressions for Its Error Term

Two Sharp Perturbed Midpoint Inequalities

In this study, two new sharp perturbed midpoint inequalities are proved by establishing proper kernel functions. These results enlarge applicability of the corresponding quadrature rules with respect to the obtained error bounds. Applications in numerical integration are also given.

Ostrowski type inequalities for functions whose derivatives are $h$-convex in absolute value

Some new inequalities of Ostrowski type for functions whose derivatives are $h$-convex in modulus are given. Applications for midpoint inequalities are provided as well.

A generalized inequality of Ostrowski type for twice differentiable bounded mappings and applications

In this paper, we will improve and generalize Ostrowski type inequality for twice differentiable mappings in terms of the upper and lower bounds of the second derivative. Some well known inequalities can be derived as special cases of the inequalities obtained here. In addition, perturbed mid-point inequality and perturbed trapezoid inequality are also obtained. The obtained inequalities have immediate applications in numerical integrations where new estimates are obtained for the remainder term of the trapezoid and midpoint formulae. Applications to special means are also investigated.

Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation

Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation are given. Applications for the trapezoid and mid-point inequalities are also provided.

Two Ostrowski type inequalities for the Stieltjes integral of monotonic functions

Two integral inequalities of Ostrowski type for the Stieltjes integral are given. The first is for monotonic integrators and Hölder continuous integrands while the second considers the dual case, that is, for monotonic integrands and Hölder continuous integrators. Applications for the mid-point inequality that are useful in the numerical analysis of Stieltjes integrals are exhibited. Some connections with the generalised trapezoidal rule are also presented.

Generalizations of the Ostrowski’s inequality

Using the Taylor-Langrange formula as well as a generalization of this one, we give some generalizations of the integral midpoint inequality as well of the Ostrowski inequality for n-time differentiable mappings. A new sharp generalized weighted Ostrowski type inequality is given.

On sharp perturbed midpoint inequalities

The main purpose of this paper is to use a variant of Gr"uss inequality to obtain some perturbed midpoint inequalities. Moreover, we show that our results are sharp and precisely characterize the functions for which equality holds. Thus we provide improvements of some recent results for perturbed midpoint inequalities.

Ostrowski's inequality for vector-valued functions and applications

In this paper, we obtain some Ostrowski type inequalities for vector-valued functions which both generalise and improve the scalar case and show that the midpoint inequality is the best possible inequality in the class. A quadrature formula of the Riemann type for the Bochner integral and the error bounds are considered. Applications to operator inequalities and numerical approximation for the mild solution of inhomogeneous vector-valued differential equations are also pointed out. In the last section, a numerical example is analysed.