Scholarlink

<p>In this paper, we study the weakest possible conditions for fixed point theorems involving two classes of mappings defined by Kannan and Chatterjea. Our approach relies on the so-called CJM condition, which was originally introduced by Ćirić (Proc Am Math Soc 45(2):267–273, 1974), and later, Suzuki (J Fixed Point Theory Appl 19, 2017) showed that the CJM condition is necessary for the existence of fixed points and the convergence of all Picard sequences of Banach type mappings. Our aim is to extend Suzuki’s approach to the case of Kannan and Chatterjea mappings. In particular, in the first case, we discuss the equivalence of previously known conditions and establish that our conditions are optimal for ensuring that all Picard sequences converge to a fixed point of a mapping.</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 the weakest conditions for the existence of fixed points of Kannan and Chatterjea type contractions

  • 期刊论文

  • 发表日期：

    2026年3月3日

查看全文
  • Shunya Hashimoto,
  • Misako Kikkawa,
  • Shuji Machihara,
  • Aqib Saghir

摘要

In this paper, we study the weakest possible conditions for fixed point theorems involving two classes of mappings defined by Kannan and Chatterjea. Our approach relies on the so-called CJM condition, which was originally introduced by Ćirić (Proc Am Math Soc 45(2):267–273, 1974), and later, Suzuki (J Fixed Point Theory Appl 19, 2017) showed that the CJM condition is necessary for the existence of fixed points and the convergence of all Picard sequences of Banach type mappings. Our aim is to extend Suzuki’s approach to the case of Kannan and Chatterjea mappings. In particular, in the first case, we discuss the equivalence of previously known conditions and establish that our conditions are optimal for ensuring that all Picard sequences converge to a fixed point of a mapping.