Ostrowski type inequalities for functions whose derivatives are preinvex

Weighted Ostrowski-Grüss type inequalities

Several inequalities of Ostrowski-Gruss-type availabe in the literature are generalized by considering the weighted case of them. Involving the least concave majorant of the modulus of continuity we provide upper error bounds of such inequalities.

Inequalities of Ostrowski's type for m- and (alpha,m)- logarithmically convex functions via Riemann-Liouville Fractional integrals

In this paper, we establish some new Ostrowski's type inequalities for m- and (alpha,m)- logarithmically convex functions by using the Riemann-Liouville fractional integrals.

Ostrowski type Inequalities for m- and (alpha,m)-geometrically convex functions via Riemann-Louville Fractional integrals

In this paper, some new inequalities of Ostrowski type established for the class of m- and (alpha,m)-geometrically convex functions which are generalizations of geometric convex functions.

Some Ostrowski type inequalities for double integrals On Time Scales

The main objective of this paper is to study some Ostrowski and Trapezoid type inequalities for double integrals on Time Scales. Some other interesting inequalities are also given.

Ostrowski's Type Inequalities for Strongly-Convex Functions

In this paper, we establish Ostrowski's type inequalities for strongly-convex functions where c>0 by using some classical inequalities and elemantery analysis. We also give some results for product of two strongly-convex functions.

Generalized weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales via a parameter function

We prove generalized weighted Ostrowski and Ostrowski--Grüss type inequalities on time scales via a parameter function. In particular, our result extends a result of Dragomir and Barnett. Furthermore, we apply our results to the continuous, discrete, and quantum cases, to obtain some interesting new inequalities.

Ostrowski type inequalities for harmonically s-convex functions via fractional integrals

In this paper, a new identity for fractional integrals is established. Then by making use of the established identity, some new Ostrowski type inequalities for harmonically s-convex functions via Riemann--Liouville fractional integral are established.

Ostrowski type inequalities for s-logarithmically convex functions in the second sense via fractional integrals

In this paper, we establish some new Ostrowski type inequalities for s-logarithmically convex functions by using Riemann-Liouville fractional integrals. Some applications of our results to P.D.F.'s are given.

Two-point Ostrowski and Ostrowski-Grüss type inequalities with applications

In this work, an extension of two-point Ostrowski's formula for $n$-times differentiable functions is proved. A generalization of Taylor formula is deduced. An identity of Fink type for this extension is provided. Error estimates for the considered formulas are also given. Two-point Ostrowski-Gruss type inequalities are pointed out. An expansion of Guessab--Schmeisser two points formula for $n$-times differentiable functions via Fink type identity is established. Generalization of the main result for harmonic sequence of polynomials is established. Several bounds of the presented results are p…

Some Ostrowski's Type Inequalities for Functions whose Second Derivatives are s-Convex in the Second Sense and Applications

Some new inequalities of Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given.Applications for special means are also provided.

New sharp inequalities of Ostrowski and generalized trapezoid type for the Riemann-Stieltjes integrals and applications

In this paper, new sharp weighted generalizations of Ostrowski and generalized trapezoid type inequalities for the Riemann--Stieltjes integrals are proved. Several related inequalities are deduced and investigated. New Simpson's type inequalities for $\mathcal{RS}$--integral are pointed out. Finally, as application; an error estimation of a general quadrature rule for $\mathcal{RS}$--integral via Ostrowski--generalized trapezoid quadrature formula is given.

New Ostrowski type inequalities for m-convex functions and applications

In this paper, we establish new inequalities of Ostrowski type for functions whose derivatives in absolute value are m-convex. We also give some applications to special means of positive real numbers. Finally, we obtain some error estimates for the midpoint formula.

New inequalities of Ostrowski's type for s-convex functions in the second sense with applications

In this paper, we establish some new inequalities of Ostrowski's type for functions whose derivatives in absolute value are the class of s-convex. Some applications for special means of real numbers are also provided. Finally, some error estimates for the midpoint formula are obtained.

New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals

New identity similar to an identity of [13] for fractional integrals have been defined. Then making use of this identity, some new Ostrowski type inequalities for Riemann-Liouville fractional integral have been developed. Our results have some relationships with the results of Alomari et. al., proved in [13] [published in. Appl. Math. Lett. 23 (2010) 1071-1076] and the analysis used in the proofs is simple.

Some New Generalized Results on Ostrowski Type Integral Inequalities With Application

The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval. Some new purterbed results are obtained. Application for cumulative distribution function is also discussed.

A Weighted Ostrowski Type inequality for L$_{1}\left[ a,b\right] $ and applications

The aim of this paper is to obtain some generalized weighted Ostrowski inequalities for differentiable mappings. 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 inequalities obtained here have direct applications in Numerical Integration, Probability Theory, Information Theory and Integral Operator Theory. Some of these applications are discussed.

On the Ostrowski-Gruss Type Inequality for Twice Differentiable Functions

In this paper, we obtained some new Ostrowski-Gruss type inequalities contains twice differentiable functions.

Some Weighted Ostrowski Type Inequalities on Time Scales Involving Combination of Weighted Delta-Integral Means

In this paper we obtain some weighted generalizations of Ostrowski type inequalities on time scales involving combination of weighted Δ-integral means, i.e., a weighted Ostrowski type inequality on time scales involving combination of weighted Δ-integral means, two weighted Ostrowski type inequalities for two functions on time scales, and some weighted perturbed Ostrowski type inequalities on time scales. We also give some other interesting inequalities and recapture some known results as special cases.

Some Ostrowski and Cebysev type inequality in three variables on Time Scales

The main objective of this paper is to study some Ostrowski and Cebysev type inequalities in three variables on Time Scales

A generalization of Ostrowski type inequality for mappings whose second derivatives belong to L$_{1}\left(a,b\right) $ and applications

In this paper, we will improve and generalize inequality of Ostrowski type for mappings whose second derivatives belong to L$_{1}\left(a,b\right) $ . Some well known inequalities can be derived as special cases. In addition, perturbed mid-point inequality and perturbed trapezoid inequality are also obtained. 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.

Weighted Ostrowski Type inequality Involving Integral Means

The ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Dragomir, Wang and Cerone .The current article obtains bounds for the deviation of a function from a combination of 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 are also discussed.

凸函数的Ostrowski型不等式

An Ostrowski Type Inequality for Convex Functions

本文提出凸函数的Ostrowski型积分不等式，应用于求积法则和积分均值，并改进Hermite-Hadamard不等式，涉及概率密度函数和(HH)-散度度量。

On generalization of different type inequalities for harmonically quasi-convex functions via fractional integrals

In this paper, we obtained some new estimates on generalization of Hadamard, Ostrowski and Simpson-like type inequalities for harmonically quasi-convex functions via Riemann Liouville fractional integral.

Taylor's formula and integral inequalities for conformable fractional derivatives

We derive Taylor's Formula for conformable fractional derivatives. This is then employed to extend some recent and classical integral inequalities to the conformable fractional calculus, including the inequalities of Steffensen, Chebychev, Hermite-Hadamard, Ostrowski, and Gruss.

Some Integral Inequalities For Functions Whoose Second Derivatives Are $φ$-Convex By Using Fractional Integrals

In this paper, we obtain new estimates on generalization of Hermite-Hadamard, Simpson and Ostrowski type inequalities for functions whose second derivatives is $φ$-convex via fractional integrals.

通过柯西中值定理的若干Ostrowski型不等式

Some Ostrowski Type Inequalites via Cauchy's Mean Value Theorem

本文利用柯西中值定理推导出若干Ostrowski型不等式，并将其应用于特定函数实例，拓展了该类不等式的适用范围。

On generalization of different type inequalities for some convex functions via fractional integrals

New identity for fractional integrals have been defined. By using of this identity, we obtained new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for s-convex, quasi-convex, m-convex functions via Riemann Liouville fractional integral.

New general integral inequalities for Lipschitzian functions via Hadamard fractional integrals

In this paper, the author obtains new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for Lipschitzian functions via Hadamard fractional integrals. Some applications to special means of positive reals numbers are also given.

On generalization of different type inequalities for (α,m)-convex functions via fractional integrals

In this paper, new identity for fractional integrals have been defined. By using of this identity, we obtained new general inequalities containing all of Hadamard, Ostrowski and Simpson type inequalities for for functions whose derivatives in absolute value at certain power are (α,m)-convex via Riemann Liouville fractional integral.

New general integral inequalities for (alpha;m)-ga-convex functions via hadamard fractional integrals

In this paper, the authors gives a new identity for Hadamard fractional integrals. By using of this identity, the authors obtains new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for (alpha?;m)-GA-convex function via Hadamard fractional integral.

New estimates on generalization of some integral inequalities for s-convex functions and their applications

In this paper, a new identity for differentiable functions is derived. Thus we can obtain new estimates on generalization of Hadamard,Ostrowski and Simpson type inequalities for functions whose derivatives in absolute value at certain power are s-convex (in the second sense). Some applications to special means of real numbers are also given.

New general integral inequalities for some GA-convex and quasi-geometrically convex functions via fractional integrals

In this paper, the author introduces the concept of the quasi-geometrically convex and defines a new identity for fractional integrals. By using of this identity, author obtains new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for GA-s-convex, quasi-geometrically convex and (s,m)-GA-convex functions via Riemann Liouville fractional integral.

New inequalities for $η$-quasiconvex functions

The class of $η$-quasiconvex functions was introduced in 2016. Here we establish novel inequalities of Ostrowski type for functions whose second derivative, in absolute value raised to the power $q\geq 1$, is $η$-quasiconvex. Several interesting inequalities are deduced as special cases. Furthermore, we apply our results to the arithmetic, geometric, Harmonic, logarithmic, generalized log and identric means, getting new relations amongst them.

内积空间中Schwarz，Gruss和Bessel型不等式的进展

Advances in Inequalities of the Schwarz, Gruss and Bessel Type in Inner Product Spaces

这本专著的主要目的是综述作者最近得到的一些与Schwarz不等式、三角不等式和贝塞尔不等式的逆有关的结果。给出了实或复内积空间中正规正交向量族的Gruss型不等式。还提供了不一定正交的向量的有限序列的Boas-Bellman、Bjueri、Selberg、Heilbronn和Pecaric不等式的推广。指出著名的Ostrowski不等式在数列或实数上的两个推广以及Wagner不等式在内积空间上的推广。最后给出了内积空间中向量组的Gruss型不等式及其在离散Fourier变换和Mellin变换逼近中的自然应用。