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.

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In this paper, we establish a generalized Ostrowski-Grüss type inequality for differentiable mappings using the weighted Grüss inequality which is another generalization of inequalities established and discussed by Barnett et al.

The aim of this paper is to establish a new version of Ostrowski's type integral inequality. The results are obtained by using a new type of kernel with five sections. Applications to a composite quadrature rule and to Cumulative Distributive Functions are considered.