Some New Anderson Type <i>h</i> and <i>q</i> Integral Inequalities in Quantum Calculus

Abstract

The calculus in the absence of limits is known as quantum calculus. With a difference operator, it substitutes the classical derivative, which permits dealing with sets of functions that are non-differentiations. The theory of integral inequality in quantum calculus is a field of mathematics that has been gaining considerable attention recently. Despite the fact of its application in discrete calculus, it can be applied in fractional calculus as well. In this paper, some new Anderson type q-integral and h-integral inequalities are given using a Feng Qi integral inequality in quantum calculus. These findings are highly beneficial for basic frontier theories, and the techniques offered by technology are extremely useful for those who can stimulate research interest in exploring mathematical applications. Due to the interesting properties in the field of mathematics, integral inequalities have a tied correlation with symmetric convex and convex functions. There exist strong correlations and expansive properties between the different fields of convexity and symmetric function, including probability theory, convex functions, and the geometry of convex functions on convex sets. The main advantage of these essential inequalities is that they can be converted into time-scale calculus. This kind of inevitable inequality can be very helpful in various fields where coordination plays an important role.

Keywords

• Anderson inequality
• Feng Qi inequality
• quantum calculus
• <i>q</i>-integral
• <i>h</i>-integral