Abstract

This article introduces Kannan type and Chatterjea type perimetric contractions on quadrilaterals and explores their key properties. It provides sufficient conditions for these mappings to achieve fixed points and identifies scenarios ensuring the uniqueness of such fixed points within a complete metric space. Furthermore, the study examines the relationships between these mapping classes and other well-established ones, offering additional insights. To support the theoretical results, several illustrative examples are included. Finally, we provide a remark showing that the arguments in [Karap\i nar, RNA, 8(1):115--123, 2025] contain a gap and therefore cannot be applied to our results.

Keywords: Fixed point theorems; perimetric contraction on quadrilaterals; Kannan type perimetric contraction on quadrilaterals; Chatterjea type perimetric contraction on quadrilaterals.

MSC: 47H09, 47H10, 54E50

DOI: 10.57016/MV-JEWE9416

Pages:  1--16