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<p>The main goal of this paper is to show that if a real-valued function defined on a groupoid satisfies a certain Levi-Civita-type functional equation, then it also fulfills a Cauchy–Schwarz-type functional inequality. In particular, if the groupoid is the multiplicative structure of a commutative ring, then we can establish the existence of nontrivial additive functions satisfying inequalities connected to the multiplicative structure.</p>

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Cauchy–Schwarz-type inequalities for solutions of Levi-Civita-type functional equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月8日

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  • Zsolt Páles,
  • Mahmood Kamil Shihab

摘要

The main goal of this paper is to show that if a real-valued function defined on a groupoid satisfies a certain Levi-Civita-type functional equation, then it also fulfills a Cauchy–Schwarz-type functional inequality. In particular, if the groupoid is the multiplicative structure of a commutative ring, then we can establish the existence of nontrivial additive functions satisfying inequalities connected to the multiplicative structure.