Generalized Interval-Valued Convexity in Fractal Geometry

The main goal of this study is to explain the idea of generalized interval-valued (I.V) convexity on a fractal set. We first define the basic operations for a generalized interval of Rs with 0<s≤1. Then, we expand the idea of (I.V) Riemann integration to (I.V) local fractal integration, which sets the stage for further research. This is followed by the proof of new Jensen, Hermite, Hadamard, Pachpatte, and Fejer inequalities that are (I.V) and have to do with the generalized class of (I.V) convexity defined over the fractal domain. We furnish validation through visual and comparative approaches. Our outcomes are the refinement of many existing results, indicating that they are fruitful. In fractal settings, this is the first paper to work on (I.V) convexity and some set-valued versions of Hermite–Hadamard-type containments.