A perspective on Banach and Kannan mappings contracting the perimeter of triangles in interpolative metric spaces - Banerjee, Anish; Mondal, Pratikshan; Kanta Dey, Lakshmi; Sintunavarat, Wutiphol (Nonlinear Analysis: Modelling and Control, 2026)
This article delves into several well-known mappings within the framework of interpolative metric spaces. To demonstrate the genuine generalization of metric spaces by interpolative metric spaces, various illustrative examples are provided. The properties of mappings that contract the perimeter of triangles are examined, and a necessary and sufficient condition for the existence of fixed points is established for such mappings, supported by relevant examples. Additionally, the study explores generalized Kannan-type mappings and generalizes a fixed point result of metric spaces in the setting of interpolative metric spaces. Further examples are provided in support of our result. Furthermore, an adequate condition for the uniqueness of the fixed points is proposed.
Keywords: fixed points; interpolative metric spaces; mapping contracting perimeter of triangles; generalized Kannan-type mappings