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<p>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 the Simpson-, Hermite– Hadamard-, midpoint-, trapezoid-, and Bullen-type inequalities for multiplicatively convex functions. Moreover, we provide some numerical examples and computational analysis of these newly established inequalities in order 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.</p>

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Generalization of Some Integral Inequalities in Multiplicative Calculus with Their Computational Analysis

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Abdul Mateen,
  • Zhiyue Zhang,
  • Muhammad Aamir Ali,
  • Michal Fečkan

摘要

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 the Simpson-, Hermite– Hadamard-, midpoint-, trapezoid-, and Bullen-type inequalities for multiplicatively convex functions. Moreover, we provide some numerical examples and computational analysis of these newly established inequalities in order 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.