A note on the paper "Contraction mappings in $b$-metric spaces" by Czerwik

TL;DR

This paper addresses and corrects a proof in Czerwik's 1993 work on contraction mappings within $b$-metric spaces, ensuring mathematical accuracy in this area of metric space theory.

Contribution

It provides a necessary correction to an existing proof in the theory of contraction mappings in $b$-metric spaces, clarifying the mathematical foundation.

Findings

Corrected proof of Theorem 1 in Czerwik's paper

Clarification of contraction mappings in $b$-metric spaces

Ensured accuracy of foundational results in the field

Abstract

In this paper we correct an inaccuracy that appears in the proof of Theorem 1. in Czerwik's article "Contraction mappings in $b$-metric spaces.", Acta Math. Inform. Univ. Ostraviensis, 1:5--11, 1993.