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The aim of this paper is to obtain some generalized weighted Ostrowskiinequalities for differentiable mappings. Some well known inequalities can bederived as special cases of the inequalities obtained here. In addition,perturbed mid-point inequality and perturbed trapezoid inequality are alsoobtained. The inequalities obtained here have direct applications in NumericalIntegration, Probability Theory, Information Theory and Integral OperatorTheory. Some of these applications are discussed.

A Weighted Ostrowski Type inequality for L$_{1}\left[ a,b\right] $ and applications