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arXiv · 2510.23952

Fixed Point Theorems for Relaxed Asymptotic Contractions via Two Quasi-Metrics

Jie Shi
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Abstract

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.

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Jie Shi. 2025-10-28. Fixed Point Theorems for Relaxed Asymptotic Contractions via Two Quasi-Metrics. https://arxiv.org/abs/2510.23952

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