扰动度量空间中的Hardy-Rogers和Jungck型不动点定理、稳定性及数据依赖性
Hardy-Rogers and Jungck Type Fixed Point Theorems in Perturbed Metric Spaces, Stability and Data Dependence
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中文总结 AI 辅助
研究在扰动度量空间中建立Hardy-Rogers和Jungck型不动点定理，探讨比\(P\)被\(d\)均匀吸收更弱的条件，证明相关稳定性等结果，推导先验误差估计，为弱相容对建立Jungck型定理。
中文摘要 AI 辅助
本文在扰动度量空间中建立了Hardy-Rogers和Jungck型不动点定理，其中观测距离\(D\)与精确度量\(d\)由非负扰动\(P\)隔开。我们研究了一个比主导条件下\(P\)被\(d\)均匀吸收更弱的要求，仅对出现压缩系数的点对施加该要求。我们表明，没有这样的条件且\(T\)无连续性假设时，完备扰动度量空间上的扰动Banach压缩可能没有不动点。我们还证明了Ulam-Hyers稳定性、适定性和数据依赖性结果，其中残差以观测距离\(D\)度量，所有常数明确，且我们推导了可从观测数据计算的Picard和Jungck迭代的先验误差估计。Jungck型定理是针对弱相容对建立的。
英文摘要
In this paper we establish Hardy-Rogers and Jungck type fixed point theorems in perturbed metric spaces, where the observed distance $D$ is separated from the exact metric $d$ by a nonnegative perturbation $P$. Rather than the uniform absorption of $P$ by $d$ required under domination, we examine a weaker demand, imposed only on the pairs of points that appear with a contractive coefficient. We show that without some such condition, and without a continuity hypothesis on $T$, a perturbed Banach contraction on a complete perturbed metric space may fail to have a fixed point. We further prove Ulam-Hyers stability, well-posedness, and data dependence results in which residuals are measured in the observed distance $D$, with all constants explicit, and we derive a priori error estimates for the Picard and Jungck iterations computable from observed data. The Jungck type theorem is established for weakly compatible pairs.
