Exploring Local Fractional Integral Inequalities Through Biparametric Analysis

In this paper, we investigate a class of biparametrized integral inequalities in the setting of local fractional calculus on fractal sets. Motivated by earlier results in [27, 39], we derive a new integral identity associated with a three-point Newton–Cotes formula involving two parameters. A noteworthy feature of this formula is that, through suitable choices of the parameters, it unifies a broad family of one-point, two-point, and three-point quadrature rules. Based on this identity, we establish several new inequalities for functions whose first-order local fractional derivatives satisfy generalized s-convexity assumptions. Our results not only extend a number of existing inequalities in the literature, but also recover several known estimates as particular cases. To illustrate the effectiveness of the theoretical findings, we present an example supported by two- and three-dimensional graphical representations, together with some applications related to quadrature formulas and special means.