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<p>We investigate the coincidence set of generalized lines and generalized monotone functions, when these notions are induced by an <i>n</i>-parameter Beckenbach family. It turns out that the coincidence set is either an interval or a finite set of at most <i>n</i> elements. Moreover, we show that this set can have exactly <i>k</i> elements if <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2379_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="108" /> </InlineMediaObject> <EquationSource Format="TEX">\(k\in \{1,\dots ,n\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>∈</mo> <mo stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>n</mi> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation> and the underlying family is an extended and complete Chebyshev-system.</p>

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The Coincidence Set of Generalized Lines and Generalized Monotone Functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月5日

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  • Mihály Bessenyei,
  • Norbert Tóth

摘要

We investigate the coincidence set of generalized lines and generalized monotone functions, when these notions are induced by an n-parameter Beckenbach family. It turns out that the coincidence set is either an interval or a finite set of at most n elements. Moreover, we show that this set can have exactly k elements if \(k\in \{1,\dots ,n\}\) k ∈ { 1 , ⋯ , n } and the underlying family is an extended and complete Chebyshev-system.