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<p>In this work, in the setting of a vector-valued metric space <i>X</i>, the fixed point inclusion <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2025_2758_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="123" /> </InlineMediaObject> <EquationSource Format="TEX">\(x\in G(x), x\in X\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>∈</mo> <mi>G</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi>x</mi> <mo>∈</mo> <mi>X</mi> </mrow> </math></EquationSource> </InlineEquation> governed by a multi-valued operator <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2025_2758_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="90" /> </InlineMediaObject> <EquationSource Format="TEX">\(G:X\multimap X\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>:</mo> <mi>X</mi> <mo>⊸</mo> <mi>X</mi> </mrow> </math></EquationSource> </InlineEquation> satisfying a weak contraction type condition on its graph is studied. Some stability results are obtained and the coincidence point problem involving two multi-valued operators is also studied. The best proximity point problem in vector-valued metric spaces is finally discussed.</p>

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Existence and stability theorems in vector-valued metric spaces for fixed point and coincidence point problems governed by multi-valued weak contractions

  • 期刊论文

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  • 发表日期：

    2025年6月27日

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  • Adrian Petruşel,
  • Gabriela Petruşel

摘要

In this work, in the setting of a vector-valued metric space X, the fixed point inclusion \(x\in G(x), x\in X\) x ∈ G ( x ) , x ∈ X governed by a multi-valued operator \(G:X\multimap X\) G : X ⊸ X satisfying a weak contraction type condition on its graph is studied. Some stability results are obtained and the coincidence point problem involving two multi-valued operators is also studied. The best proximity point problem in vector-valued metric spaces is finally discussed.