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<p>The underlying aims of this work are first to state vectorial version of a class of mappings, named <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1218_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\({\textsf{G}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="sans-serif">G</mi> </math></EquationSource> </InlineEquation>-contraction, and second to show the existence of best proximity points for such mappings in a graphical vector metric, which can entail a large number of former results. One fundamental issue that can be distinguished between this work and previous researches is that it can also involve all of results stated by taking comparable and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1218_Article_IEq5.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-close elements. </p>

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Vectorially \({\textsf{G}}\)-contraction mappings and best proximity points

  • 期刊论文

  • 发表日期：

    2025年4月24日

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  • K. Fallahi,
  • A. Petruşel,
  • G. Soleimani Rad

摘要

The underlying aims of this work are first to state vectorial version of a class of mappings, named \({\textsf{G}}\) G -contraction, and second to show the existence of best proximity points for such mappings in a graphical vector metric, which can entail a large number of former results. One fundamental issue that can be distinguished between this work and previous researches is that it can also involve all of results stated by taking comparable and \(\varepsilon \) ε -close elements.