In this paper we derive new weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales. Some other interesting inequalities on time scales are also given as special cases.

X iv :0 70 5. 35 56 v1 [ m at h. FA ] 2 4 M ay 2 00 7 New Generalization of Perturbed Ostrowski Type Inequalities and Applications Wen-jun Liu, Qiao-ling Xue, Jian-wei Dong Abstract: Generalizations of Ostrowski type inequality for functions of Lipschitzian type are established. Applications in numerical integration and cumulative distribution functions are also given.

This is the fifth and last in our series of notes concerning some classical inequalities such as the Ostrowski, Simpson, Iyengar, and Ostrowski–Grüss inequalities in R. In the last note, we propose an improvement of the Ostrowski–Grüss inequality which involves 3n knots where n = 1 is an arbitrary numbers. More precisely, suppose that fxkgk1⁄41 1⁄20;1 ; fykg n k1⁄41 1⁄20;1 , and fakg n k1⁄41 1⁄...

Recently, the research for the Ostrowski type and Grüss type inequalities has been paid much attention by many authors. The Ostrowski type inequality, which was originally presented by Ostrowski in [1], can be used to estimate the absolute deviation of a function from its integral mean, while the Grüss inequality [2] can be used to estimate the absolute deviation of the integral of the product ...

In this paper, verified extension of the Ostrowski method which calculates the enclosure solutions of a given nonlinear equation is introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the scheme. Keywords—Iinterval analysis, nonlinear equations, Ostrowski method.

Making use of an identity of Dragomir and Barnett, proved in [13] [published in J. Indian Math. Soc. (N.S.), 66 (1999), No. 1-4, 237-245], some new Ostrowski and Čebyšev type inequalities involving two functions have been developed. Bounds obtained for the new established Ostrowski and Čebyšev type inequalities are of interest and are better than the bounds available in the literature for these...

In this paper, we establish a new integral identity involving differentiable functions, and then use the newly established to prove some Ostrowski–Mercer-type inequalities for convex functions. It is also demonstrated that are generalizations of Ostrowski inside literature. There applications special means real numbers given.

Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.

for all x ∈ [a, b]. This inequality is a connection between the Ostrowski inequality [12] and the Grüss inequality [13]. It can be applied to bound some special mean and some numerical quadrature rules. For other related results on the similar integral inequalities please see the papers [6, 10, 11, 14] and the references therein. The aim of this paper is to extend a generalizations of Ostrowski...

The solution to a nonlinear equation is found in this study by combining classical and powerful method. Basically, it well known that the Homotopy Continuation Method (HCM) method has been used for solving problem of A new approach introduced which as Ostrowski (Ostrowski-HCM) with purpose overcome divergence arises from Ostrowski’s when bad initial guess used. To put simply, derivative given f...