Scholarlink

<p>This paper develops a unified and extended framework for contraction-type mappings in metric spaces by introducing extended unified interpolative Ćirić–Reich–Rus type <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>,</mo> <mi>F</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(\alpha ,\beta ,F)$</EquationSource> </InlineEquation>-contractions together with their <i>r</i>-order counterparts. Within this general setting, rigorous existence and uniqueness results for fixed points of self-mappings are established. The proposed approach not only subsumes numerous classical and contemporary contraction principles as particular cases, but also elucidates the structural relationships among them. The scope and effectiveness of the new framework are further demonstrated through applications to nonlinear integral equations, confirming its relevance and potential for broader analytical investigations.</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

Extended unified interpolative and hybrid \((\alpha ,\beta ,F)\) contractions in metric spaces and applications to integral equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月30日

查看全文
  • Kastriot Zoto,
  • Abdelhamid Moussaoui,
  • Stojan Radenović

摘要

This paper develops a unified and extended framework for contraction-type mappings in metric spaces by introducing extended unified interpolative Ćirić–Reich–Rus type ( α , β , F ) $(\alpha ,\beta ,F)$ -contractions together with their r-order counterparts. Within this general setting, rigorous existence and uniqueness results for fixed points of self-mappings are established. The proposed approach not only subsumes numerous classical and contemporary contraction principles as particular cases, but also elucidates the structural relationships among them. The scope and effectiveness of the new framework are further demonstrated through applications to nonlinear integral equations, confirming its relevance and potential for broader analytical investigations.