Generalization of some integral inequalities in multiplicative calculus with their computational analysis - Mateen, Abdul; Zhang, Zhiyue; Ali, Muhammad Aamir; Fečkan, Michal (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.9We focus on generalizing some multiplicative integral inequalities for twice differentiable functions. First, we derive a multiplicative integral identity for multiplicatively twice differentiable functions. Then, with the help of the integral identity, we prove a family of integral inequalities, such as Simpson, Hermite–Hadamard, midpoint, trapezoid, and Bullen types inequalities for multiplicatively convex functions. Moreover, we provide some numerical examples and computational analysis of these newly established inequalities to prove the validity  of the results for multiplicatively convex functions. The generalized forms obtained in our research offer valuable tools for researchers in various fields.