Scholarlink

<p>The purpose of this paper is to further investigate generalized <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_879_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\( \alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-nonexpansive mappings. We establish that this class of mappings admits an approximate fixed point sequence in the setting of Banach spaces. Additionally, for <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_879_Article_IEq5.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\( \alpha &gt; 0 \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, we prove that these mappings are asymptotically regular on nonempty bounded subsets of Banach spaces. Finally, we prove a new existence result for generalized <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_879_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-nonexpansive mappings.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On generalized \(\alpha \)-nonexpansive mappings in Banach spaces

  • 期刊论文

  • 发表日期：

    2025年10月29日

查看全文
  • Deepak Khantwal,
  • Rajendra Pant

摘要

The purpose of this paper is to further investigate generalized \( \alpha \) α -nonexpansive mappings. We establish that this class of mappings admits an approximate fixed point sequence in the setting of Banach spaces. Additionally, for \( \alpha > 0 \) α > 0 , we prove that these mappings are asymptotically regular on nonempty bounded subsets of Banach spaces. Finally, we prove a new existence result for generalized \(\alpha \) α -nonexpansive mappings.