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Subordinate Semimetric Spaces and Fixed Point Theorems
Journal of Mathematics, 2018 We introduce the concept of subordinate semimetric space. Such notion includes the concept of RS-space introduced by Roldán and Shahzad; therefore the concepts of Branciari’s generalized metric space and Jleli and Samet’s generalized metric space are ...
José Villa-Morales
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Hutchinson’s theorem in semimetric spaces [PDF]
Journal of Fixed Point Theory and Applications, 2021 One of the important consequences of the Banach fixed point theorem is Hutchinson’s theorem which states the existence and uniqueness of fractals in complete metric spaces.
Mátyás Kocsis, Zsolt P'ales
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Two metrics on rooted unordered trees with labels [PDF]
Algorithms for Molecular Biology, 2022 Background The early development of a zygote can be mathematically described by a developmental tree. To compare developmental trees of different species, we need to define distances on trees.
Yue Wang
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Contingency Space: A Semimetric Space for Classification Evaluation
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022 In Machine Learning, a supervised model’s performance is measured using the evaluation metrics. In this study, we first present our motivation by revisiting the major limitations of these metrics, namely one-dimensionality, lack of context, lack of ...
Azim Ahmadzadeh +3 more
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Completeness in semimetric spaces [PDF]
Pacific Journal of Mathematics, 1984 This interesting paper compares various forms of completeness in semimetric spaces in face of certain ''continuity properties'' of distance functions. Two such properties are developability: lim d(x\({}_ n,p)=\lim d(y_ n,p)=0\) implies lim d(x\({}_ n,y_ n)=0\), and 1- continuity: for any q, lim d(x\({}_ n,p)=0\) implies lim d(x\({}_ n,q)=d(p,q)\).
F. Galvin, S. Shore
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Cauchy sequences in semimetric spaces [PDF]
Proceedings of the American Mathematical Society, 1972 As the main result we prove that every semimetrizable space has a semimetric for which every convergent sequence has a Cauchy subsequence. This result is used to show that a T 1 {T_1} space X is semimetrizable if and only if it is a pseudo-open π \pi -image of a metric space.
D. Burke
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A REGULAR LINDELOF SEMIMETRIC SPACE WHICH HAS NO COUNTABLE NETWORK [PDF]
Proceedings of the American Mathematical Society, 1970 A completely regular semimetric space M M is constructed which has no σ \sigma -discrete network. The space M M constructed has the property that every subset of M M of cardinality 2 ℵ 0
E. Berney
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Local linear modelling of the conditional distribution function for functional ergodic data
Mathematical Modelling and Analysis, 2022 The focus of functional data analysis has been mostly on independent functional observations. It is therefore hoped that the present contribution will provide an informative account of a useful approach that merges the ideas of the ergodic theory and ...
Somia Ayad +3 more
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Uniqueness of best proximity pairs and rigidity of semimetric spaces
Journal of Fixed Point Theory and Applications, 2022 For arbitrary semimetric space $$(X, d)$$ ( X , d ) and disjoint proximinal subsets $$A$$ A , $$B$$ B of $$X$$ X we define the proximinal graph as a bipartite graph with parts $$A$$ A and $$B$$ B whose edges $$\{a, b\}$$ { a , b } satisfy the equality ...
O. Dovgoshey, R. Shanin
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Characterizations of K- Semimetric Spaces
Sultan Qaboos University Journal for Science [SQUJS], 2003 In this paper, we prove, for a space X , the following are equivalent: 1. X is a D 1 space with a regular- G δ -diagonal, 2. X is a D 2 space with a regular- G δ -diagonal, 3. X is a semi-developable space with G δ (3) -diagonal, 4.
A. Mohamad
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