Some properties and inequalities for generalized class of harmonical Godunova-Levin function via center radius order relation

There are many benefits derived from the speculation regarding convexity in the fields of applied and pure science. According to their definitions, convexity and integral inequality are linked concepts. The construction and refinement of classical inequalities for various classes of convex and nonconvex functions have been extensively studied. In convex theory, Godunova-Levin functions play an important role, because they make it easier to deduce inequalities when compared to convex functions. Based on Bhunia and Samanta's total order relation, harmonically cr- $h$-Godunova-Levin function is defined in this paper. Utilizing center order (CR) relationship, various types of inequalities can be introduced. (CR)-order relation enables us to derive some Hermite-Hadamard ( $\mathcal{H}\mathcal{.}\mathcal{H}$) inequality along with a Jensen-type inequality for harmonically $h$-Godunova-Levin interval-valued functions (GL- $\mathcal{I}\mathcal{V}\mathcal{F}\mathcal{S}$). Many well-known and new convex functions are unified by this kind of convexity. For further verification of the accuracy of our findings, we provide some numerical examples.