New Approach to Weighted Newton‐Type Inequalities Using Riemann–Liouville Fractional Integrals

ABSTRACT In this investigation paper, we present some weighted inequalities Newton‐type for various classes of functions utilizing Riemann–Liouville fractional integrals. The study begins by introducing a positive weighted function to derive a key integral equality essential for proving the main results. By applying this equality along with Riemann–Liouville fractional integrals, we establish several weighted Newton‐type inequalities for some function classes, including Lipschitzian functions, bounded functions, convex functions, and functions of bounded variation. The results offer valuable insights into the significance of inequalities of Newton‐type and give some directions for future research. The findings extend those presented in earlier works.