Applications of ball spaces theory: Fixed point theorems in semimetric spaces and ball convergence

0567216 - MÚ 2024 RIV CH eng J - Článek v odborném periodiku
Nowakowski, Piotr - Turobos, F.
Applications of ball spaces theory: Fixed point theorems in semimetric spaces and ball convergence.
Journal of Fixed Point Theory and Applications. Roč. 25, č. 1 (2023), č. článku 31. ISSN 1661-7738. E-ISSN 1661-7746
Grant CEP: GA ČR(CZ) GF20-22230L
Institucionální podpora: RVO:67985840
Klíčová slova: b-metric spaces * ball spaces * fixed point theorems * semimetric spaces
Obor OECD: Pure mathematics
Impakt faktor: 1.8, rok: 2022
Způsob publikování: Open access
https://doi.org/10.1007/s11784-022-01030-y

In the paper, we apply some of the results from the theory of ball spaces in semimetric setting. This allows us to obtain fixed point theorems which we believe to be unknown to this day. As a byproduct, we obtain the equivalence of some different notions of completeness in semimetric spaces where the distance function is 1-continuous. In the second part of the article, we generalize the Caristi-Kirk results for b-metric spaces. Additionally, we obtain a characterization of semicompleteness for 1-continuous b-metric spaces via a fixed point theorem analogous to a result of Suzuki. In the epilogue, we introduce the concept of convergence in ball spaces, based on the idea that balls should resemble closed sets in topological sets. We prove several of its properties, compare it with convergence in semimetric spaces and pose several open questions connected with this notion.
Trvalý link: https://hdl.handle.net/11104/0338498