JAI functional contractions in relational metric spaces

Abstract

The 2015 fixed point result on rs-relational metric spaces due to Alam and Imdad [J. Fixed Point Th. Appl., 17 (2015), 693-702] is equivalent with the classical Banach Contraction Principle [Fund. Math., 3 (1922), 133-181]. This is also valid for the 1961 statement in metric spaces due to Edelstein [Proc. Amer. Math. Soc., 12 (1961), 7-10], or the 2005 fixed point result in quasi-ordered metric spaces obtained by Nieto and Rodriguez-Lopez [Order, 22 (2005), 223-239].