GENERALIZED PETROVIČ INEQUALITY AND ITS RELATED ESTIMATIONS IN SUPERQUADRATICITY ON THE FRACTAL SPACE WITH APPLICATIONS

This study considers the concept of generalized superquadratic functions within fractal spaces. The inequalities derived from these functions demonstrate greater precision compared to those obtained from convex functions. The work begins with the presentation of the generalized Petrovič inequality in fractal spaces. Two identities for differentiable generalized superquadratic functions are then established. Using these identities and the generalized Petrovič inequality, fractal versions of midpoint and trapezoid-type inequalities are derived for differentiable generalized superquadratic functions. The findings are supported by reduced cases and graphical representations based on select examples. Additionally, the research is enriched by incorporating special means and functions within fractal spaces. These results contribute significantly to the existing literature, providing enhanced insights and extending the understanding of inequalities in fractal contexts.