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. (Inequality theory and applications, pp. 24-30, 2001), S. S. Dragomir and S. Wang (Comput. Math. Appl. 33:15-22, 1997) and A. Rafiq et al. (JIPAM. J. Inequal. Pure Appl. Math. 7(4):124, 2006). Perturbed midpoint and trapezoid inequalities are obtained. Some applications in different weights are given. This inequality is extended to account for applications in numerical integration.
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Hussain et al. (2013) studied this question.