Search

Some recently obtained generalization of weighted Montgomery identity is considered and used to obtain the new weighted generalizations of the Čebišev and Ostrowski inequality.

[1] A. CIVLJAK, LJ. DEDIC AND M. MATIC, On Ostrowski and Euler-Gruss type inequalities involving measures, Journal of Mathematical Inequalities, 1, 1 (2007), 65–81. [2] A. CIVLJAK, LJ. DEDIC AND M. MATIC, On an integration-by-parts formula for measures, Journal of Inequalities in Pure and Applied Mathematics, 8, 4 (2007), Article 93, 13 pp. [3] A. CIVLJAK, LJ. DEDIC AND M. MATIC, Euler-Gruss type inequalities involving measures, International Series of Numerical Mathematics, Birkhauser Verlag Basel/Switzerland, Vol. 157 (2008), 109– 120, 2008. [4] A. CIVLJAK, LJ. DEDIC AND M. MATIC,Euler harmonic identities for measures, Nonlinear Functional Analysis and Applications, 12, 3 (2007), 343–361. [5] M. MATIC, J. PECARIC AND N. UJEVIC,Generalizations of weighted version of Ostrowski’s inequality and some related results, Journal of Inequalities and Applications, 5 (2000), 639–666.

In this paper, we establish some inequalities which improve some Ostrowski type inequalities. Applications for Euler’s Beta mapping and special means are also given.

For a sequence $(P_{; ; ; k}; ; ; (t), k\geq 0)$ of polynomials satisfying the condition $$ P_{; ; ; k}; ; ; ^{; ; ; \prime }; ; ; (t)=P_{; ; ; k-1}; ; ; (t), \text{; ; ; }; ; ; k\geq 1 ; \text{; ; ; \ }; ; ; P_{; ; ; 0}; ; ; (t)=1, $$ we say that it is a harmonic sequence of polynomials. We give some generalizations of Ostrowski inequality, by using harmonic sequences of polynomials. We consider the Milovanovi\'{; ; ; c}; ; ; -Pe\v{; ; ; c}; ; ; ari\'{; ; ; c}; ; ; -Fink inequality, the Anastassiou's generalizations of the Ostrowski inequality and we give the generalizations of Ostrowski inequality via Euler harmonic identities.

In this paper we establish some new Ostrowski type integral inequalities, by using the Montgomery identity and Taylor's formula.

Some new generalizations of the integral and discrete weighted Euler identity are presented as well as related generalizations of the integral and discrete Ostrowski type inequalities.

[1] A. CIVLJAK, LJ. DEDIC AND M. MATIC, On an integration-by-parts formula for measures, To appear (submitted to International Journal of Pure and Applied Mathematics). [2] A. CIVLJAK, LJ. DEDIC AND M. MATIC, Euler-Gruss type inequalities involving measures, To appear (submitted to Elsevier, JMAA, Nov 19, 2006). [3] M. MATIC, J. PECARIC AND N. UJEVIC, Generalizations of weighted version of Ostrowski’s inequality and some related results, Journal of Inequalities and Applications, 2000, Vol. 5, pp. 639–666.

Generalizations of Euler identities involving µ-harmonic sequences of functions with respect to a real Borel measure µ are established. Some Ostrowski type inequalities for functions of various classes are proved.

In this paper we show some generalizations of estimations of difference of two integral means, Milovanović-Pečarić-Fink inequality.

Few different versions of Landau type inequalities are given, each using the Ostrowski inequality or Ostrowski type inequalities.

Generalizations of Euler identities involving μ -harmonic sequences of functions with respect to a real Borel measure μ are established. Some Ostrowski type inequalities for functions of various classes are proved.Also an inequality of Grüss type for a real Borel measure μ is proved and some related Euler-Grüss type inequalities are given.

We present discrete analogue of the weighted Montgomery identity as well as it's generalizations for finite and infinite sequences. Further we use theese identities to obtain some discrete Ostrowski type inequalities and the estimates of the difference between two arithmetic means.

Generalizations of estimations of difference of two integral means are given, by using Euler-type identities.

We introduced and illustrated a technique that the error estimates in numerical integration can be essentially improved by working with more refined norms in concrete cases. For example, the error estimates for Simpson type numerical integration can be written as the norm of f' in the function space l1(4)(Lp, w), (the weighted amalgam spaces or Block-Lp-spaces).

Some generalizations of the Ostrowski inequality, the Milovanovic-Pecaric-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.

We present optimal upper bounds for the deviation of a fuzzy continuous function from its fuzzy average over [a,b] Ì R, error is measured in the D-fuzzy metric. The established fuzzy Ostrowski type inequalities are sharp, in fact attained by simple fuzzy real number valued functions. These inequalities are given for fuzzy Hölder and fuzzy differentiable functions and these facts are reflected in their right-hand sides.

Some generalizations of Ostrowski inequality are given, by using some Euler identities involving harmonic sequences of polynomials.

Some generalizations of Ostrowski inequality for Hölder functions and functions with bounded derivatives are given.

[1] N. S. BARNETT AND S. S. DRAGOMIR, Issues of estimation in the monitoring of constant flow continuous streams, RGMIA, Research report collection, Vol. 2, No. 3 (1999), pp. 275–282 [2] D. S. MITRINOVIC, J. PECARIC AND A. M. FINK, Inequalities involving functions and their integrals and derivatives, Kluwer Acad. Publ., Dordrecht, 1991. [3] A. OSTROWSKI, Uber die Absolutabweichung einer differentierbaren Funktionen von ihren Integralmittelwort, Comment. Math. Helv., 10(1938), 226–227.

The unified treatment of some inequalities for convex functions of higher order.

We give an integral analogue of the Ostrowski inequality and several extensions, allowing in particular for multiple linear constraints

Some Ostrowski type inequalities are given for the Stieltjes integral where the integrand is absolutely continuous while the integrator is of bounded variation. The case when |f′| is convex is explored. Applications for the mid-point rule and a generalised trapezoid type rule are also presented.

In this paper, we study some Ostrowski-like type inequalities proposed by Huy and Ngo. We give some improvements of these inequalities which are inspired by a result established recently.

Optimal upper bounds are given for the deviation of a value of a multivariate function of a fractional space from its average, over convex and compact subsets of RN,N≥2. In particular we work over rectangles, balls and spherical shells. These bounds involve the supremum and L∞ norms of related multivariate fractional derivatives of the function involved. The inequalities produced are sharp, namely they are attained. This work has been motivated by the works of Ostrowski [A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funcktion von ihrem Integralmittelwert, Commentarii Mathematici Helvetici 10 (1938) 226–227], 1938, and of the author [G.A. Anastassiou, Fractional Ostrowski type inequalities, Communications in Applied Analysis 7 (2) (2003) 203–208], 2003.

The main aim of this paper is to establish an Ostrowski type inequality on H-type groups using the L∞ norm of the horizontal gradient. The work has been motivated by the work of Anastassiou and Goldstein in [G.A. Anastassiou, J.A. Goldstein, Higher order Ostrowski type inequalities over Euclidean domains, J. Math. Anal. Appl. 337 (2008) 962–968].

We study the Cauchy--Schwarz and some related inequalities in a semi-inner product module over a $C^*$-algebra $\A$. The key idea is to consider a semi-inner product $\A$-module as a semi-inner product $\A$-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 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 element of a $C^*$-algebra, converges to its pseudo-inverse., 18 pages, to appear in J. Math. Anal. Appl. (JMAA)

A connection between generalized Montgomery identity, Bernoulli polynomials and Euler identity is esablished. Using this connection, certain strict improvements of some Ostrowski type inequalities are obtained.