@article{Shi2026, 
author = {Jie Shi},
title = {Fixed point theorems for relaxed asymptotic contractions via two quasi-metrics},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {22983-22998},
keywords = {fixed point, relaxed asymptotic contractions, lower quasi-metric, upper quasi-metric, local uniform convergence, Boyd-Wong condition},
url = {https://www.sciopen.com/article/10.3934/math.2026926},
doi = {10.3934/math.2026926},
abstract = {We introduced a new class of asymptotic contractions that employed two quasi-metrics defined directly in terms of the underlying mapping. The contraction condition compared these two quantities via a sequence of bounding functions that converged locally uniformly to a Boyd-Wong function. This framework relaxed the hypotheses of Kirk's asymptotic fixed point theorem and theoretically contained it as a special case. Assuming only the continuity of the map and the boundedness of some orbit in a complete metric space, we proved both the existence and uniqueness of a fixed point, along with the convergence of all iterates to that point.}
}