Some integral inequalities involving q-h fractional integral operator

In this work, we extend several well-known classical inequalities by applying a newly defined q-h operator over finite intervals. Specifically, we generalize the Cauchy-Schwarz integral inequality for double integrals, Grüss integral inequality, Korkine identity, and Grüss-Čebyšev integral inequality. These generalizations provide tighter bounds and enhanced applicability in the framework of quantum calculus. The q-h-integral, which combines features of the q-integral and h-integral, serves as a unifying tool to connect and extend existing results. Furthermore, we examine special cases to demonstrate the broader scope of these inequalities. Our findings highlight the versatility of the q-h-operator in refining and expanding the mathematical framework of integral inequalities in quantum calculus.