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The well-known Taylor polynomial is used to construct the identities coming from Popoviciu type inequalities for convex functions via the Green function. The bounds for the new identities are found using the Čebyšev functional to develop the Grüss and Ostrowski type inequalities. Further, more exponential convexity together with Cauchy means is presented for linear functionals associated with the obtained inequalities. [ABSTRACT FROM AUTHOR]

We consider inequalities which incorporate both Jensen and Ostrowski type inequalities for functions with absolutely continuous n-th derivatives. We provide applications of these inequalities for divergence measures. In particular, we obtain inequalities involving higher order X-divergence [ABSTRACT FROM AUTHOR]

We provide new inequalities of Jensen-Ostrowski type, by considering bounds for the magnitude of $\int_{\Omega} f\circ g \, d\mu-f ( \zeta ) - ( \int_{\Omega }g\, d\mu-\zeta ) f^{\prime} ( \zeta ) -\frac {1}{2}\lambda \int_{\Omega} ( g-\zeta ) ^{2}\, d\mu$, $\zeta\in [a,b]$, with various assumptions on the absolutely continuous function $f:[a,b]\rightarrow\mathbb{C}$ and a μ-measurable function g, and a complex number λ. Inequalities of Ostrowski and Jensen type are obtained as special cases, by setting $\lambda=0$ and $\zeta =\int_{\Omega}g\, d\mu$, respectively. In particular, we obtain some bounds for the discrepancy in Jensen's integral inequality. Applications of these inequalities for f-divergence measures are also given. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we provide inequalities of Jensen–Ostrowski type, by providing bounds for the magnitude of ∫ Ω ( f ∘ g ) d μ − f ( ζ ) − ∫ Ω ( g − ζ ) f ′ ∘ g d μ + 1 2 λ ∫ Ω ( g − ζ ) 2 d μ , for various assumptions on the absolutely continuous function f : [ a , b ] → C , ζ ∈ [ a, b ], λ ∈ C , and a μ -measurable function g on Ω . Special cases are considered to provide some inequalities of Jensen type, as well as Ostrowski type, in measure-theoretic (probabilistic) form. Applications for f -divergence measure in information theory are also considered. [ABSTRACT FROM AUTHOR]

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

In this paper, some exponential Pompeiu's type inequalities for complex-valued absolutely continuous functions are provided. They are applied to obtain some new Ostrowski type inequalities. [ABSTRACT FROM AUTHOR]

In this paper amongst other, we show that if f : [a, b] → ℝ is absolutely continuous on [a, b] and Φ: ℝ → ℝ is convex (concave) on ℝ, then ... for any x ∈ [a, b]. Natural applications for power and exponential functions are provided as well. Bounds for the Lebesgue p-norms of the deviation of a function from its integral mean are also given. [ABSTRACT FROM AUTHOR]

In this paper, we establish several new inequalities for s-convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with an Ostrowski type integral inequality in the literature. [ABSTRACT FROM AUTHOR]

We provide a new Ostrowski-type inequality involving functions of two independent variables, as well as some related results. [ABSTRACT FROM AUTHOR]

In this paper we obtain some new generalizations of Ostrowski type inequalities on time scales involving combination of Δ-integral means, i.e., a new Ostrowski type inequality on time scales involving combination of Δ-integral means, two Ostrowski type inequalities for two functions on time scales, and some new perturbed Ostrowski type inequalities on time scales. We also give some other interesting inequalities as special cases. [ABSTRACT FROM AUTHOR]

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 and best possible in case . Applications for the Hadamard fractional integrals are given. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We further interpret and simplify earlier produced fractional Ostrowski and Grüss type inequalities involving several functions. [ABSTRACT FROM AUTHOR]

In this paper, the authors established several new inequalities of the Beesack–Wirtinger type for different kinds of differentiable convex functions. Furthermore, we generalized our results for functions that are n-times differentiable convex. Finally, many interesting Ostrowski- and Chebyshev-type inequalities are given as well. [ABSTRACT FROM AUTHOR]

Recently, there have been many proven results of the Ostrowski–Grüss-type inequality regarding the error bounds for the Chebyshev functional when the functions or their derivatives belong to L p spaces. In the existing literature, the main assumption in the weight-type results is that the derivative of the function is bounded by two constant functions. The aim of our paper is to extend those results in a way that the derivative of the function is bounded by two functions in L p spaces. Furthermore, we give some new error estimations of the Chebyshev functional and applications to the one-point weight integral formulas. [ABSTRACT FROM AUTHOR]

In this paper, we use the Riemann-Liouville fractional integrals to establish some new integral inequalities of Ostrowski-Grüss type. From our results, the classical Ostrowski-Grüss type inequalities can be deduced as some special cases. [ABSTRACT FROM AUTHOR]

We establish new inequalities for the cumulative distribution function, the incomplete special function, the expectation, the variance and the k-th order moments. [ABSTRACT FROM AUTHOR]

Abstract: We compute the optimal constants of Ostrowski-like inequalities involving n knots given by Huy and Ngô. [Copyright &y& Elsevier]

Abstract: In this paper, we study some Ostrowski-like type inequalities proposed by Huy and Ngô. We give some improvements of these inequalities which are inspired by a result established recently. [Copyright &y& Elsevier]

Abstract: Integration with weight functions is used in countless mathematical problems such as: approximation theory and spectral analysis, statistical analysis and the theory of distributions. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Barnett et al. in 2001 and Rafiq et al. in 2006. We also discuss some other interesting inequalities in special cases. Perturbed midpoint and trapezoid inequalities are also obtained. Some applications in numerical integration are also given. [Copyright &y& Elsevier]

In this paper a Grüss type inequalities for Riemann-Stieltjes integral are proved. Applications to the approximation problem of the Riemann-Stieltjes are also pointed out. [ABSTRACT FROM AUTHOR]

Several inequalities for a companion of Ostrowski inequality for absolutely continuous mappings whose first derivatives absolute value are convex (resp. concave) are established. Applications to a composite quadrature rule, to p.d.f.'s, and to special means are provided. [ABSTRACT FROM AUTHOR]

Here we derive very general multivariate tight integral inequalities of Chebyshev–Grüss, Ostrowski types and of comparison of integral means. These are based on well-known Sobolev integral representation of a function. Our inequalities engage ordinary and weak partial derivatives of the involved functions. We also give their applications. On the way to prove our main results we derive important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. Our results expand to all possible directions. [ABSTRACT FROM AUTHOR]

Abstract: Very general univariate Ostrowski type inequalities are presented regarding Banach space valued functions. They provide norm estimates for the deviation of the average of the function from its vector values, and they involve the th order vector derivative, , with respect to , . On the way to prove our results we establish useful functional vector identities. Using our vector Ostrowski inequalities we derive the vector Landau inequalities. [Copyright &y& Elsevier]

Here we derive very general univariate tight integral inequalities of Chebyshev-Grüss, Ostrowski types, for comparison of integral means and Information theory. These are based on well-known Sobolev integral representations of a function. Our inequalities engage ordinary and weak derivatives of the involved functions. We give also applications. On the way to prove our main results we derive important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. Our results expand to all possible directions. [ABSTRACT FROM AUTHOR]

Abstract: Here, we give univariate and multivariate representations of the Montgomery type for hybrid functions on time scales. Based on these, we establish univariate and multivariate Ostrowski type inequalities on time scales domains. These compare the average of a function to its values. The estimates involve the higher order delta and nabla derivatives and partial derivatives. We finish with applications on the time scales and . [Copyright &y& Elsevier]

Abstract: We study the Cauchy–Schwarz and some related inequalities in a semi-inner product module over a -algebra . The key idea is to consider a semi-inner product -module as a semi-inner product -module with respect to another semi-inner product. In this way, we improve some inequalities such as the Ostrowski inequality and an inequality related to the Gram matrix. The induced semi-inner products are also related to the notion of covariance and variance. Furthermore, we obtain a sequence of nested inequalities that emerges from the Cauchy–Schwarz inequality. As a consequence, we derive some interesting operator-theoretical corollaries. In particular, we show that the sequence arising from our construction, when applied to a positive invertible element of a -algebra, converges to its inverse. [Copyright &y& Elsevier]