Perimetric Contraction on Quadrilaterals

摘要

In this article, we introduce a four point analogue of the Banach contraction principle and establish sufficient conditions for such mappings to possess fixed point(s) in complete metric spaces. Notably, the classical Banach contraction principle emerges as a special case of our results. We present several non-trivial examples that not only validate our theorems but also reveal that quadrilateral perimetric contractions need not imply other well-known contraction types. Furthermore, we extend our analysis to obtain fixed point theorems in non-complete metric spaces. Lastly, we address a recent result linking mappings contracting the perimeters of triangles in metric spaces to Banach-type contractions in 𝐺-metric spaces.