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In the present paper, some error bounds for weighted Ostrowski–Grüss type inequalities are found by using the weighted Čebyšev functional and Diaz–Metcalf inequality. These bounds give some better and new estimates. Applications are also obtained for numerical integration. Furthermore, this paper recaptures some previous established results as its special cases.

Estimates for weighted Ostrowski–Grüss type inequalities with applications