A fixed point theorem for contractive mappings that characterizes metric completeness

2012/07/26 by Abtahi, Mortaza
#54H25 (Primary) 54E50 (Secondary) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1207.6207

Abstract

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.

Related

• Fixed points and completeness in metric and in generalized metric spaces
• On contractive mappings in b_v(s)-metric spaces
• A Suzuki-type fixed point theorem for nonlinear contractions
• Weakly contractive maps in altering metric spaces
• On contractive mappings