On contractive mappings

1973/10/01 by Michael A. Geraghty · 11 citations
Mathematics · Physics and Astronomy · #Fixed Point Theorems Analysis #Advanced Differential Geometry Research

paper · doi:10.1090/s0002-9939-1973-0334176-5

Abstract

The Cauchy condition for convergence of a contractive iteration in a complete metric space is replaced by an equivalent functional condition. Many generalizations of the Banach-Neumann contractive mapping principle follow.

Citations

• On nonlinear contractions

Cited by

• Fixed points and completeness in metric and in generalized metric spaces
• A Suzuki-type fixed point theorem for nonlinear contractions
• Coincidence and Common Fixed Point Results for Contraction Type Maps in Partially Ordered Metric Spaces
• Function contractive maps in triangular symmetric spaces
• Topological developments of F-metric spaces
• Existence and uniqueness of fixed point for ordered contraction type operator in Banach Space
• Fixed point theorems for Meir-Keeler type contractions in metric spaces
• Positive solutions of fractional integral equations by the technique of measure of noncompactness. [europepmc]
• Common fixed point theorems for ( T , g ) F -contraction in b -metric-like spaces. [europepmc]
• Fixed point-based stability analysis of climate and Langevin models. [europepmc]
• Solving age-dependent infectious diseases and tumor growth models using the contraction approach. [europepmc]

Related

• A fixed point theorem for contractive mappings that characterizes metric completeness
• On contractive mappings in b_v(s)-metric spaces
• Fixed points theorems for unsaturated and saturated classes of contractive mappings in Banach spaces
• Function contractive maps in partial metric spaces
• Some extensions of Banach' CP in G-metric spaces