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<p>This paper develops new integral inequalities that bound the deviation of a differentiable function from its mean using <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^1\)</EquationSource> </InlineEquation>-bounded first and second derivatives. By leveraging monotonicity properties of these bounding functions, we refine classical Ostrowski-type results to obtain sharper and more general estimates. Several corollaries, including constant-bound cases, are also presented with rigorous proofs based primarily on Taylor expansions and integral inequalities.</p>

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Integral bounds for differentiable functions via monotone derivative constraints and their applications

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Mehmet Zeki Sarikaya

摘要

This paper develops new integral inequalities that bound the deviation of a differentiable function from its mean using \(L^1\) -bounded first and second derivatives. By leveraging monotonicity properties of these bounding functions, we refine classical Ostrowski-type results to obtain sharper and more general estimates. Several corollaries, including constant-bound cases, are also presented with rigorous proofs based primarily on Taylor expansions and integral inequalities.