Scholarlink

<p>This paper investigates a class of composition operators: the nonlinear operator <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3313_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>T</mi> <mo>=</mo> <mi>A</mi> <mo>∘</mo> <mi>B</mi> </math></EquationSource> <EquationSource Format="TEX">$T=A\circ B$</EquationSource> </InlineEquation> and the sum-type operator <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3313_Article_IEq3.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="114" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>T</mi> <mo>=</mo> <mi>A</mi> <mo>∘</mo> <mi>B</mi> <mo>+</mo> <mi>C</mi> </math></EquationSource> <EquationSource Format="TEX">$T=A\circ B+C$</EquationSource> </InlineEquation>, where <i>A</i>, <i>B</i>, and <i>C</i> are either single or bivariate operators. Here, “∘” denotes the composition operation between operators <i>A</i> and <i>B</i>. By applying cone theory and monotone iterative techniques, we establish the existence and uniqueness of fixed points of <i>T</i> within the set <i>P</i>. Additionally, we develop two successively monotone iterative sequences to approximate the unique positive fixed point. Finally, by leveraging the fixed point theorem for composition operators derived in this paper, we analyze a class of boundary value problems for Riemann-Liouville fractional differential equations involving <i>p</i>-Laplacian operators.</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

Fixed point results on nonlinear composition operators \(A\circ B\) and applications

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月14日

查看全文
  • Bibo Zhou,
  • Yiping Du

摘要

This paper investigates a class of composition operators: the nonlinear operator T = A ∘ B $T=A\circ B$ and the sum-type operator T = A ∘ B + C $T=A\circ B+C$ , where A, B, and C are either single or bivariate operators. Here, “∘” denotes the composition operation between operators A and B. By applying cone theory and monotone iterative techniques, we establish the existence and uniqueness of fixed points of T within the set P. Additionally, we develop two successively monotone iterative sequences to approximate the unique positive fixed point. Finally, by leveraging the fixed point theorem for composition operators derived in this paper, we analyze a class of boundary value problems for Riemann-Liouville fractional differential equations involving p-Laplacian operators.