Scholarlink

<p>In this paper, we introduce and study a new class of multivalued mappings called <i>set-valued convex contractions of order two</i>. This notion extends the classical concept of Nadler contractions by incorporating two control parameters that jointly govern the contractive behavior of the mapping through both the Pompeiu–Hausdorff metric and the underlying metric of the space. We establish a fixed point theorem for such mappings in complete metric spaces under the assumption of upper semicontinuity. Our result properly generalizes Nadler’s fixed point theorem and provides a unified framework encompassing several existing types of multivalued contractions. Illustrative examples are provided to demonstrate that the new class of contractions is strictly broader than the classical one. Possible extensions and applications of the main result to more general metric-like spaces are also discussed.</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 set-valued convex contractions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月9日

查看全文
  • Ishak Altun,
  • Ümran Başar

摘要

In this paper, we introduce and study a new class of multivalued mappings called set-valued convex contractions of order two. This notion extends the classical concept of Nadler contractions by incorporating two control parameters that jointly govern the contractive behavior of the mapping through both the Pompeiu–Hausdorff metric and the underlying metric of the space. We establish a fixed point theorem for such mappings in complete metric spaces under the assumption of upper semicontinuity. Our result properly generalizes Nadler’s fixed point theorem and provides a unified framework encompassing several existing types of multivalued contractions. Illustrative examples are provided to demonstrate that the new class of contractions is strictly broader than the classical one. Possible extensions and applications of the main result to more general metric-like spaces are also discussed.