Quantum Weddle's type inequalities for convex functions with their computational analysis and applications

Abstract

In this paper, quantum Weddle’s type inequalities for convex functions have been derived, involving the extension of the classical results in the framework of q-calculus. We present new conditions that describe the behaviour of convex functions using the quantum calculus, which undermines the systematical theory of the related phenomena in theoretical and applied mathematics. We also investigate some aspects of these inequalities, such as scaling and translation, and demonstrate how some of the inequalities are connected to other existing inequalities in the intersection of convex analysis and optimization. Furthermore, numerical and graphical solutions to the inequalities applied to real-life problems are given, along with an illustration of the computation and the connection to the relevant inequalities. Therefore, the findings of the present work are also useful in extending the theory of convex functions.