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<p>This paper presents a general identity including two real parameters for three times differentiable functions. By using this equality, we prove several inequalities by using diverse function classes such as convex function, bounded function, Lipschitzian function, and function of bounded variation. By special choices of the parameters in the obtained results, we present some well-known inequalities: midpoint inequality, trapezoid inequality, Milne inequality, Bullen inequality, and Simpson inequality.</p>

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Parameterized inequalities based on three times differentiable functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月21日

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  • Bouharket Benaissa,
  • Noureddine Azzouz,
  • Hüseyin Budak

摘要

This paper presents a general identity including two real parameters for three times differentiable functions. By using this equality, we prove several inequalities by using diverse function classes such as convex function, bounded function, Lipschitzian function, and function of bounded variation. By special choices of the parameters in the obtained results, we present some well-known inequalities: midpoint inequality, trapezoid inequality, Milne inequality, Bullen inequality, and Simpson inequality.