Fractal Modeling of Generalized Weighted Pre-Invex Functions with Applications to Random Variables and Special Means

This article introduces certain algebraic properties of generalized (h˜1,h˜2)-pre-invex functions on Rℵ(0<ℵ≤1). A new fractal weighted integral identity is established and further employed to obtain several Ostrowski-type results in the fractal setting for functions whose first derivatives in the modulus belong to the generalized (h˜1,h˜2)-pre-invex functions’s class. An illustrative example is presented to validate the theoretical findings. Moreover, applications of the main results are derived in connection with generalized random variables and various special means, highlighting the effectiveness and potential scope of the proposed approach.