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.