A generalized Ostrowski-Grüss type inequality for bounded differentiable mappings and its applications

Journal of inequalities and applications

Sabir Hussain¹ 

关键词: Ostrowski inequality;    Grüss inequality;    weight function;    numerical integration;   

DOI  :  10.1186/1029-242X-2013-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY