Functional Contractions in Relational Metric Spaces

The 2015 fixed point result on rs-relational metric spaces, due to Alam and Imdad [J. Fixed Point Theory Appl. 17 (2015), 693–702], is equivalent to the classical Banach contraction principle [Fund. Math. 3 (1922), 133–181]. The same is true for the 1961 statement in metric spaces, due to Edelstein [Proc. Amer. Math. Soc. 12 (1961), 7–10], and for the 2005 fixed point result in quasi-ordered metric spaces obtained by Nieto and Rodríguez-López [Order 22 (2005), 223–239].