Connected \(\epsilon\)-chainable sets and existence results (Q6169332)

In the setting of \(\epsilon\)-chainable metric spaces, the authors introduce \((\epsilon - \rho - \sigma)\) uniformly local weak contractions and obtain some results on the existence of fixed points. Some examples show that the results are satisfied with \(\epsilon\)-chainable metric spaces, but they do not validate in the setting of metric spaces and generalized metric spaces.