Abstract
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 rho>1 as well as rho<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.