A Generalisation of an Ostrowski Inequality in Inner Product Spaces

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.

On the weighted Ostrowski type integral inequality for double integrals

In this paper, we establish new an inequality of weighted Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.

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 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.

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.

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.

绝对连续函数的 Ostrowski 不等式的一些伴随不等式及其应用

Some Companions of Ostrowski's Inequality for Absolutely Continuous Functions and Applications

本文给出绝对连续函数的 Ostrowski 不等式伴随形式，并应用于复合求积规则与概率密度函数。

通过Pompeiu中值定理的Ostrowski型不等式

An Inequality of Ostrowski Type via Pompeiu's Mean Value Theorem

利用Pompeiu中值定理给出了积分均值的不等式界，并应用于求积公式和特殊均值。

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 the Bombieri Inequality in Inner Product Spaces

New results related to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.

On the Boas-Bellman Inequality in Inner Product Spaces

New results related to the Boas-Bellman generalisation of Bessel's inequality in inner product spaces are given.

Some Bombieri Type Inequalities in Inner Product

Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.

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

The main aim of this monograph is to survey some recent results obtained by the author related to reverses of the Schwarz, triangle and Bessel inequalities. Some Gruss' type inequalities for orthonormal families of vectors in real or complex inner product spaces are presented as well. Generalizations of the Boas-Bellman, Bombieri, Selberg, Heilbronn and Pecaric inequalities for finite sequences of vectors that are not necessarily orthogonal are also provided. Two extensions of the celebrated Ostrowski's inequalities for sequences or real numbers and the generalization of Wagner's inequality in…

Cheeger's differentiation theorem via the multilinear Kakeya inequality

Suppose that $(X,d,μ)$ is a metric measure space of finite Hausdorff dimension and that, for every Lipschitz $f \colon X \to \mathbb R$, $\operatorname{Lip}(f,\cdot)$ is dominated by every upper gradient of $f$. We show that $X$ is a Lipschitz differentiability space, and the differentiable structure of $X$ has dimension at most $\dim_{\mathrm{H}} X$. Since our assumptions are satisfied whenever $X$ is doubling and satisfies a Poincaré inequality, we thus obtain a new proof of Cheeger's generalisation of Rademacher's theorem. Our approach uses Guth's multilinear Kakeya inequality for neighbour…

Gradient estimates for heat kernels and harmonic functions

Let $(X,d,μ)$ be a doubling metric measure space endowed with a Dirichlet form $\E$ deriving from a "carré du champ". Assume that $(X,d,μ,\E)$ supports a scale-invariant $L^2$-Poincaré inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for $p\in (2,\infty]$: (i) $(G_p)$: $L^p$-estimate for the gradient of the associated heat semigroup; (ii) $(RH_p)$: $L^p$-reverse Hölder inequality for the gradients of harmonic functions; (iii) $(R_p)$: $L^p$-boundedness of the Riesz transform ($p<\infty$); (iv) $(GBE)$: a generalised Bakry-É…