Fundamentals of Right Hahn q ‐Symmetric Calculus and Related Inequalities

Hahn symmetric quantum calculus is a generalization of symmetric quantum calculus. Motivated by the Hahn symmetric quantum calculus, we present the right Hahn symmetric derivative and integral, which are novel definitions for derivative and definite integral in Hahn symmetric quantum calculus. Additionally, we distinguish between the classical, Hahn, left, and right Hahn symmetric quantum derivatives of a function using an example. Moreover, we develop a few fundamental definite integral results that are crucial for deriving the Hermite–Hadamard inequalities at various points. Furthermore, we construct H ö lder′s and Minkowski inequalities using the definition of a definite right Hahn symmetric quantum integral. Finally, all newly obtained findings change to right q ‐symmetric calculus when we insert w = 0.