Synchronization Analysis of Multiple Integral Inequalities Driven by Steklov Operator

We construct a subclass of Copson’s integral inequality in this article. In order to achieve this goal, we attempt to use the Steklov operator for generalizing different inequalities of the Copson type relevant to the situations ρ>1 as well as ρ<1. We demonstrate the inequalities with the guidance of basic comparison, Holder’s inequality, and the integration by parts approach. Moreover, some new variations of Hardy’s integral inequality are also presented with the utilization of Steklov operator. We also formulate many remarks and two examples to show the novelty and authenticity of our results.

Some new integral inequalities via Steklov operator

Hardy and Copson type inequalities have been studied by a large number of authors during the twentieth century and has motivated some important lines of study which are currently active. A large number of papers have been appeared involving Copson and Hardy inequalities (see [2-16] for more details). In this paper some Hardy-Steklov and Copson-Steklov type integral inequalities were established.