Error bounds of multiplicative Boole’s type inequalities for twice differentiable functions with applications to numerical integration

This paper introduces a new multiplicative integral identity for functions that are twice differentiable in the multiplicative sense. Using this identity, we establish Boole-type inequalities under the assumption of convexity within the framework of multiplicative calculus. The results provide improved absolute error bounds for integral approximations compared to those obtained through classical calculus, especially for higher-degree polynomials. To demonstrate the usefulness of these inequalities, we apply them to numerical quadrature formulas and special means. Finally, numerical examples accompanied by graphical representations are presented to validate the theoretical findings and demonstrate their practical relevance.