Weighted Ostrowski Type Inequalities Research Articles

Weighted Ostrowski type inequalities for co-ordinated convex functions

In this paper, utilizing an identity given by Yıldız and Sarıkaya in (Yildiz and Sarikaya in Int. J. Anal. Appl. 13(1):64–69, 2017), we establish some weighted Ostrowski type inequalities for co-ordinated convex functions in a rectangle from the plane mathbb{R} ^{2}. Moreover, as special cases of our main results, we give some weighted Hermite–Hadamard type inequalities. The results given in this paper provide generalizations of some result established in earlier works.

Weighted Ostrowski type inequalities via Montgomery identity involving double integrals on time scales

<abstract><p>In this paper, the Montgomery identity is generalized for double integrals on time scales by employing a novel analytical approach to develop the generalized Ostrowski type integral inequalities involving double integrals. Some inimitable cases are discussed for different parameters and parametric functions. Moreover, applications to some particular time scales are also presented.</p></abstract>

Multiple Diamond-Alpha Integral in General Form and Their Properties, Applications

In this paper, we introduce the concept of n-dimensional Diamond-Alpha integral on time scales. In particular, it transforms into multiple Delta, Nabla and mixed integrals by taking different values of alpha. Some of its properties are explored, and the relationship between it and the multiple mixed integral is provided. As an application, we establish some weighted Ostrowski type inequalities through the new integral. These new inequalities expand some known inequalities in the monographs and papers, and in addition, furnish some other interesting inequalities. Examples of Ostrowski type inequalities are posed in detail at the end of the paper.

Generalizations of Ostrowski type inequalities via Hermite polynomials

We present new generalizations of the weighted Montgomery identity constructed by using the Hermite interpolating polynomial. The obtained identities are used to establish new generalizations of weighted Ostrowski type inequalities for differentiable functions of class C^{n}. Also, we consider new bounds for the remainder of the obtained identities by using the Chebyshev functional and certain Grüss type inequalities for this functional. By applying those results we derive inequalities for the class of n-convex functions.

Weighted Ostrowski type inequalities by Lidstone polynomials

Weighted Ostrowski type inequalities by Lidstone polynomials

Generalization of weighted Ostrowski type inequalities by Abel-Gontscharoff polynomial

Generalization of weighted Ostrowski type inequalities by Abel-Gontscharoff polynomial

On generalization of weighted Ostrowski type inequalities for functions of bounded variation

In this paper, some generalization of weighted Ostrowski type integral inequalities for mappings of bounded variation are obtained and some interesting inequalities as special cases are given.

Generalized Weighted Ostrowski, Trapezoid and Grüss Type Inequalities on Time Scales

Abstract In this article, using two parameters, we obtain generalizations of a weighted Ostrowski type inequality and its companion inequalities on an arbitrary time scale for functions whose first delta derivatives are bounded. Our work unifies the continuous and discrete versions and can also be applied to the quantum calculus case.

A Perturbed Version of General Weighted Ostrowski Type Inequality and Applications

The main purpose of this paper is to derive some new generalizations of weighted Ostrowski type inequalities. The new established inequalities are carried out for a twice differentiable mapping in different L p spaces. Applications throught considering Gruss type inequality and numerical integration are also provided.

On Weighted Montgomery Identity for k Points and Its Associates on Time Scales

The purpose of this paper is to establish a weighted Montgomery identity for k points and then use this identity to prove a new weighted Ostrowski type inequality. Our results boil down to the results of Liu and Ngô if we take the weight function to be the identity map. In addition, we also generalize an inequality of Ostrowski-Grüss type on time scales for k points. For k=2, we recapture a result of Tuna and Daghan. Finally, we apply our results to the continuous, discrete, and quantum calculus to obtain more results in this direction.

On weighted Ostrowski type inequalities for functions of two variables with bounded variation

On weighted Ostrowski type inequalities for functions of two variables with bounded variation

A new weighted Ostrowski type inequality on arbitrary time scale

In this paper, we prove a new weighted generalized Montgomery identity and then use it to obtain a weighted Ostrowski type inequality for parameter function on an arbitrary time scale. In addition, the real, discrete and quantum cases are considered.

On New Weighted Ostrowski Type inequalities Involving Integral Means over End Intervals and Application

The aim of this paper is to establish new inequalities using weight function which generalizes the inequalities of Dragomir, Wang and Cerone. In this article we obtain bounds for the deviation of a function from a combination of weighted integral means over the end intervals covering the entire interval. A variety of earlier results are recaptured as particular instances of the current development. Applications for cumulative distribution function is also discussed.

Weighted Montgomery identity for the fractional integral of a function with respect to another function

Abstract. We present a weighted Montgomery identity for the fractional integral of a function f with respect to another function g and use it to obtain weighted Ostrowski type inequalities for fractional integrals involving functions whose first derivatives belong to Lp spaces. These inequalities are generally sharp in case p > 1 $p>1$ and best possible in case p = 1 $p=1$ . Applications for the Hadamard fractional integrals are given.

On the weighted Ostrowski type inequalities for double integrals

In this paper, we obtain weighted Ostrowski type inequalities for function whose second order partial derivatives are bounded.

Some Weighted Ostrowski Type Inequalities

Some weighted Ostrowski type inequalities are established via the weighted Montgomery identity. A generalized weighted Montgomery identity is also considered, and thus a different proof of an Ostrowski type inequality is presented.

Weighted Ostrowski type inequalities for functions with one point of nondifferentiability

We present a weighted generalization involving derivatives of arbitrary order of the recently obtained Ostrowski type inequality for functions with one point of nondifferentiability.

Weighted Ostrowski Type Inequalities with Application to Onepoint Integral Formula

We develop weighted generalization of the recently obtained Ostrowski type inequalities for continuous functions with eventually one point of non-differentiability. We apply these general result for some famous weight functions.

Another generalization of weighted Ostrowski type inequality for mappings of bounded variation

A new generalization of weighted Ostrowski type inequality for mappings of bounded variation with a unified sharp bound is established.

Generalizations of weighted Ostrowski type inequalities for mappings of bounded variation and their applications

In this paper, we establish some generalizations of weighted Ostrowski type inequalities.