Wirtinger type inequalities for higher order differentiable functions

Abstract

In this work, we establish a Wirtinger type inequality which gives the relation between the integral of square of a function and the integral of square of its any order derivative via Taylor's formula. Then, we provide a similar inequality for mappings that are elements of L-r space with r > 1. Also, we indicate that special cases of these inequalities give some results presented in the earlier works.