Symmetric quantum calculus in interval valued frame work: operators and applications

The primary emphasis of the present study is to introduce some novel characterizations of the interval-valued $(\mathcal{I}.\mathcal{V})$ right symmetric quantum derivative and antiderivative operators relying on generalized Hukuhara difference. To continue the study, we start with the concept of symmetric differentiability in the interval-valued sense and explore some important properties. Furthermore, through the utilization of the $(\mathcal{I}.\mathcal{V})$ symmetric derivative operator, we develop the right-sided $(\mathcal{I}.\mathcal{V})$ integral operator and explore its key properties. Also, we establish various $(\mathcal{I}.\mathcal{V})$ trapezium-like inequalities by considering the newly proposed operators and support line. Later on, we deliver another proof of the trapezium inequality through an analytical approach. Also, we present the numerical and visual analysis for the verification of our results.