Some new estimates of well known inequalities for $(h_1,h_2)$-Godunova-Levin functions by means of center-radius order relation

In this manuscript, we aim to establish a connection between the concept of inequalities and the novel Center-Radius order relation. The idea of a Center-Radius (CR)-order interval-valued Godunova-Levin (GL) function is introduced by referring to a total order relation between two intervals. Consequently, convexity and nonconvexity contribute to different kinds of inequalities. In spite of this, convex theory turns to Godunova-Levin functions because they are more efficient at determining inequality terms than other convexity classes. Our application of these new definitions has led to many classical and novel special cases that illustrate the key findings of the paper. Using total order relations between two intervals, this study introduces CR- $(h_1,h_2)$-Goduova-Levin functions. It is clear from their properties and widespread usage that the Center-Radius order relation is an ideal tool for studying inequalities. This paper discusses various inequalities based on the Center-Radius order relation. With the CR-order relation, we can first derive Hermite-Hadamard ( $\mathcal{H}\mathcal{.}\mathcal{H}$) inequalities and then develop Jensen-type inequality for interval-valued functions ( $\mathcal{I}\mathcal{V}\mathcal{F}\mathcal{S}$) of type $(h_1,h_2)$-Godunova-Levin function. Furthermore, the study includes examples to support its conclusions.