Contributions to the Steffensen integral double inequality

In this article, we contribute to the understanding and development of the Steffensen integral double inequality. First, we show how some of its extensions can themselves be extended by a well-configured version of the classical Steffensen integral double inequality. We also establish variants of the Steffensen integral right inequality involving three or more functions. Finally, we introduce new generalized versions of this right inequality by exploiting the monotonicity and convexity assumptions of an intermediate function. Several numerical examples are given to illustrate the theoretical results.