TY  - JOUR
AU  - Shi, Jie
PY  - 2026
TI  - Fixed point theorems for relaxed asymptotic contractions via two quasi-metrics
JO  - AIMS Mathematics
SP  - 22983
EP  - 22998
VL  - 11
IS  - 7
AB  - 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.
UR  - https://doi.org/10.3934/math.2026926
DO  - 10.3934/math.2026926