Analysis on Symmetric Post-Quantum Integral Inequalities

In mathematics, the integral inequalities are crucial. Research on this topic has recently been conducted using the $$\varvec{q}$$ -, $$(\varvec{p},\varvec{q})$$ -, and symmetric $$\varvec{q}$$ -calculus. In this manuscript, first, we consider the left endpoint of the interval and introduce the new concept of integration and derivatives in dual basic symmetric quantum calculus. Moreover, we derive symmetric post-quantum variants of integral inequalities, i.e., $$\widetilde{(\varvec{p},\varvec{q})}$$ -H $$\ddot{o}$$ lder, $$\widetilde{(\varvec{p},\varvec{q})}$$ - Minkowski, $$\widetilde{(\varvec{p},\varvec{q})}$$ -Hermite–Hadamard, and some kinds of $$\widetilde{(\varvec{p},\varvec{q})}$$ -Hermite–Hadamard inequalities. Finally, we give a graphical analysis of our obtained results by selecting certain parameters in different variants of newly introduced $$\widetilde{(\varvec{p},\varvec{q})}$$ -Hermite–Hadamard-type inequalities via support line.