Abstract:
We establish some new weighted integral identities and use them to prove a number of inequalities of Ostrowski type. Among other results, we generalize one result related to the weighted version of the Ostrowski's inequality of Pe ari and Savi (Zbornik radova VA KoV (Beograd), 9 (1983), 171–202) as well as the recent result of Roumeliotis et al. (RGMIA, 1(1) (1998)). We also show that the recent Anastassiou's generalization (Proc. Amer. Math. Soc., 123 (1995), 3775–3781) of the Ostrowski's inequality is a special case of some results from this paper.

Abstract:
In this paper we obtain some weighted generalizations of Ostrowski type inequalities on time scales involving combination of weighted {\Delta}-integral means, i.e., a weighted Ostrowski type inequality on time scales involving combination of weighted {\Delta}-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.

Abstract:
In this note, we establish new an inequality of Ostrowski-type involving functions of two independent variables by using certain integral inequalities.

Abstract:
In this note, we establish new an inequality of Ostrowski-type involving functions of two independent variables by using certain integral inequalities.

Abstract:
We present Montgomery identity for Riemann-Liouville fractional integral as well as for fractional integral of a function with respect to another function . We further use them to obtain Ostrowski type inequalities involving functions whose first derivatives belong to spaces. These inequalities are generally sharp in case and the best possible in case . Application for Hadamard fractional integrals is given. 1. Introduction The following Ostrowski inequality is well known [1]: It holds for every whenever is continuous on and differentiable on with derivative bounded on ; that is, Ostrowski proved this inequality in 1938, and since then it has been generalized in a number of ways. Over the last few decades, some new inequalities of this type have been intensively considered together with their applications in numerical analysis, probability, information theory, and so forth. This inequality can easily be proved by using the following Montgomery identity (see, for instance, [2]): where is the Peano kernel, defined by The Riemann-Liouville fractional integral of order is defined by where is a gamma function When (5) is the Riemann definition of fractional integral. In case , fractional integral reduces to classical integral. In [3], the following Montgomery identity for fractional integrals is obtained. Theorem 1. Let , differentiable on , integrable on , and . Then, the following identity holds: where In [3], the authors used this identity to obtain the following Ostrowski type inequality for fractional integrals. Theorem 2. Let , differentiable on , and for every ; then, the following Ostrowski inequality holds: These results were further generalized in [4], while in [5] generalizations are obtained for fractional integral of a function with respect to another function (defined in Section 3). In the present paper, we give another, simpler new generalization of Montgomery identity for Riemann-Liouville fractional integral of order , which holds for a larger set of ; that is, . We also obtain Montgomery identity for fractional integral of a function with respect to another function . We further use these identities to obtain generalizations of Ostrowski inequality for fractional integrals of a function with respect to another function for functions whose first derivatives belong to spaces. These inequalities are generally sharp in case and the best possible in case . As a special case, application for Hadamard fractional integrals is given. 2. Montgomery Identity for Fractional Integrals In this section we give another, simpler new generalization of

Abstract:
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.