Generalization of some integral inequalities in multiplicative calculus with their computational analysis

• Дата: 2025
• Автори: Mateen, Abdul, Zhang, Zhiyue, Ali, Muhammad Aamir, Fečkan, Michal
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2025
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/7765
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.9 We 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.