A fixed point theorem for contractive mappings that characterizes metric   completeness
  Inspired by the work of Suzuki in [Proc. Amer. Math. Soc. 136 (2008), 1861--1869] we prove a fixed point theorem for contractive mappings that generalizes a theorem of Geraghty in [Proc. Amer. Math. Soc., 40 (1973), 604--608] and characterizes metric completeness. 
Mortaza Abtahi
math.GN