Fixed Point Theorems for Relaxed Asymptotic Contractions via Two Quasi-Metrics
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911599707553792 |
|---|---|
| author | Shi, Jie |
| author_facet | Shi, Jie |
| contents | We introduce a new class of asymptotic contractions that employs two quasi-metrics defined directly in terms of the underlying mapping. The contraction condition compares these two quantities via a sequence of bounding functions that converge locally uniformly to a Boyd-Wong function. This framework relaxes the hypotheses of Kirk's asymptotic fixed point theorem and strictly contains it as a special case. Assuming only the continuity of the map and the boundedness of some orbit in a complete metric space, we prove both the existence and uniqueness of a fixed point, along with the convergence of all iterates to that point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed Point Theorems for Relaxed Asymptotic Contractions via Two Quasi-Metrics Shi, Jie Functional Analysis 47H10 F.2.2 We introduce a new class of asymptotic contractions that employs two quasi-metrics defined directly in terms of the underlying mapping. The contraction condition compares these two quantities via a sequence of bounding functions that converge locally uniformly to a Boyd-Wong function. This framework relaxes the hypotheses of Kirk's asymptotic fixed point theorem and strictly contains it as a special case. Assuming only the continuity of the map and the boundedness of some orbit in a complete metric space, we prove both the existence and uniqueness of a fixed point, along with the convergence of all iterates to that point. |
| title | Fixed Point Theorems for Relaxed Asymptotic Contractions via Two Quasi-Metrics |
| topic | Functional Analysis 47H10 F.2.2 |
| url | https://arxiv.org/abs/2510.23952 |