Integral inequality bounding the weighted absolute deviation of an n-dimensional function

The author states and proves an integral inequality that bounds the weighted integrated absolute deviation of a differentiable n-dimensional real function over an interval, relative to any value the function takes within the interval. Examples illustrate the utility of the inequality. In particular, the inequality is shown to be applicable to certain set-theoretic signal restoration algorithms, which project an observed (degraded) signal onto a closed, convex prototype set defined by a linear filter and a suitable bound