## A linear constructive approximation for integrable functions and a parametric quadrature model based on a generalization of Ostrowski-Grüss type inequalities

### Abstract

A new generalization of Ostrowski-Grüss type inequalities, depending on a parameter $\lambda$, is introduced in order to construct a specific linear approximation for integrable functions. Some important subclasses of this inequality such as $\lambda = 1/2,1,$ and $\sqrt 2/2$ are studied separately. The generalized inequality is employed to establish a parametric quadrature model and obtain its error bounds.

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### Key words

Ostrowski-Grüss type inequalities, linear constructive approximation, numerical quadrature rules, Chebyshev functional, kernel function.

### AMS subject classifications

26D15, 65D30, 26D20, 65D32.

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