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<p>In this paper, we introduce a generalization and refinement of the Cauchy-Schwarz inequality within the framework of positive functionals. By employing elementary techniques, we sharpen the Cauchy-Schwarz inequality for real numbers, specifically for a particular class of unital positive functionals. Additionally, our results yield a variety of related inequalities, demonstrating the broader applicability of this approach.</p>

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Remark on the Cauchy-Schwarz inequality

  • 期刊论文

  • 发表日期：

    2026年3月4日

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  • R. Kumar,
  • M. Verma

摘要

In this paper, we introduce a generalization and refinement of the Cauchy-Schwarz inequality within the framework of positive functionals. By employing elementary techniques, we sharpen the Cauchy-Schwarz inequality for real numbers, specifically for a particular class of unital positive functionals. Additionally, our results yield a variety of related inequalities, demonstrating the broader applicability of this approach.