B-metric spaces, fixed points and Lipschitz functions

Abstract

The paper is concerned with b-metric and generalized b-metric spaces. One proves the existence of the completion of a generalized b-metric space and some fixed point results. The behavior of Lipschitz functions on b-metric spaces of homogeneous type, as well as of Lipschitz functions defined on, or with values in quasi-Banach spaces, is studied.

32 pages; added some results of Aimar on balls in b-metric spaces A new proof of Czerwik result is included. The paper is revised

References in corpus (3)

• A note on the paper "Contraction mappings in $b$-metric spaces" by Czerwik
• Riemann integrability under weaker forms of continuity in infinite dimensional spaces
• On Frink's metrization technique and applications

Cited by in corpus (2)

• Some remarks on the metrizability of some well known generalized metric-like structures
• On characterization of functions preserving metric-type conditions via triangular and polygonal structures