A converse of the Banach contraction principle for partial metric spaces and the continuum hypothesis
Piotr Maćkowiak
研究将 Banach 压缩原理的 Bessaga 逆命题推广至偏度量空间，并证明其相应版本与连续统假设等价。
本文提出了适用于偏度量空间的 Banach 压缩原理的 Bessaga 逆命题的一个版本，并证明了该版本与连续统假设等价。
A version of the Bessaga inverse of the Banach contraction principle for partial metric spaces is presented. Equivalence of that version and the continuum hypothesis is shown as well.
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It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present paper represents the development of some fixed point results regarding sequences of contractions in the setting of cone metric spaces over Banach algebras. Furthermore, some examples are given in order to strengthen our new concepts. Also, based on the powerful notion of a cone metric space over a Banach algebra, we present important applications to systems …
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该研究提出新型自映射PA-压缩（路径平均压缩），证明完备度量空间上连续PA-压缩有唯一不动点且Picard迭代收敛，严格推广Banach压缩原理，验证其与多种经典压缩映射独立，可捕捉逐点压缩失效时的长期压缩行为。
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本文提出循环p-φ压缩映射的概念，并研究其在不同空间中的固定点存在性和唯一性。
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本文提出Banach、Kannan、Chatterjea三类收缩的四点类似形式，推导其在完备度量空间中存在不动点的充分条件，证明经典Banach收缩原理为其特例，并给出非平凡示例验证理论结果。
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Best Proximity Point Results for Cyclic Orbital Contraction Mappings in $CAT_p(0)$ Metric Spaces
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A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric spaces that fulfill an extra regularity property. The stability of fixed points is also investigated in this setting. As applications, fixed point results are presented for several important generalizations of metric spaces.
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本文研究 Banach 空间中直径二性质与 M-理想的对偶关系，证明 M-理想的对偶继承各类 $w^*$ 直径二性质，并以反例说明逆命题不成立，进而考察 $C(K)$ 空间及其对偶。
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本文在超度量Banach空间上，给出了算子$A$的预解式条件，使得对所有自然数$m$，$\\\\|A^m\\\\|\leq 1$，即$A$为压缩算子。
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Another Perspective on Chatterjea Contraction
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本文提出了一种基于固体向量空间的锥度量空间的统一理论，并应用该理论给出了迭代压缩原理和Banach压缩原理在固体向量空间上的锥度量空间中的完整表述。
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