Perimetric contraction on quadrilaterals and related fixed point results

Abstract: In this article, we introduce a four-point analogue of Banach-type, Kannan-type, and Chatterjea-type contractions, and examine their properties. We establish sufficient conditions under which these mappings achieve fixed points in a complete metric space. Notably, the classical Banach contraction principle emerges as a special case of our results. To illustrate our theoretical findings, we present several non-trivial examples.