发表机构
Kent State University（肯特州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在b-度量空间中引入配对-Chatterjea压缩概念，建立相关不动点定理，证明其恰当扩展Chatterjea型压缩，还研究配对及配对-Kannan压缩的不动点结果，通过例子说明结果适用性，扩展推广了现有不动点定理。
AI 中文摘要
本文在b-度量空间中针对单值映射引入配对-Chatterjea压缩的概念，并在该压缩条件下建立若干不动点定理。我们证明每个Chatterjea型压缩都是配对-Chatterjea压缩，但反之不成立，由此表明后者类恰当扩展了前者类。此外，我们研究b-度量空间中配对及配对-Kannan压缩的不动点结果，给出若干具体例子以说明所得结果的适用性与尖锐性。本文的发现扩展并推广了文献中若干现有的不动点定理。
英文摘要
In this paper, we develop a fixed point framework for paired contractive mappings in complete $b$-metric spaces. We introduce the class of paired-Chatterjea contractions and establish a corresponding fixed point theorem. We further show that every Chatterjea-type contraction is a paired-Chatterjea contraction, whereas the converse implication does not hold, demonstrating that the paired formulation properly extends the Chatterjea-type class. Additionally, we establish a fixed point theorem for Paired contractions under the condition $α\in[0,1)$, thereby extending the admissible range of the contraction constant from $[0,\frac1s)$ in Bouker et al.~(2026) to [0,1). Furthermore, we examine the Paired-Kannan fixed point result of Bouker et al.~(2026) and provide an example showing that the stated coefficient condition does not guarantee the claimed fixed point conclusion in $b$-metric spaces. Motivated by this observation, we establish a corrected Paired-Kannan fixed point theorem under a complete and appropriately formulated set of hypotheses. Under suitable contractive conditions, we prove that the contractions under consideration have fixed points if and only if they have no periodic point of prime period 2. Moreover, we show that each of these contractions has at most two fixed points. Several examples are presented to illustrate our results and distinguish the proposed paired contractive mappings from existing ones.
Comments22 pages
