A Unified Approach to Several Inequalities Involving Functions and Derivatives

    loading  Checking for direct PDF access through Ovid


There are many inequalities measuring the deviation of the average of a function over an interval from a linear combination of values of the function and some of its derivatives. A general setting is given from which the desired inequalities are obtained using Hölder's inequality. Moreover, sharpness of the constants is usually easy to prove by studying the equality cases of Hölder's inequality. Comparison of averages, extension to weighted integrals and n-dimensional results are also given.

    loading  Loading Related Articles