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Start Over Subject metric space

2. Fixed point results on a metric space endowed with a finite number of graphs and applications

Creator:
Argoubi, Hajer, Samet, Bessem, and Turinici, Mihai
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
fixed point, graph, metric space, order, and cyclic map
Language:
English
Description:
In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Gradual doubling property of Hutchinson orbits

Creator:
Aimar, Hugo, Carena, Marilina, and Iaffel, Bibiana
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
metric space, doubling measure, Hausdorff-Kantorovich metric, and iterated function system
Language:
English
Description:
The classical self-similar fractals can be obtained as fixed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure is a (normal) space of homogeneous type. But the doubling property along this iteration is generally not preserved even when the starting point, and of course the limit point, both have the doubling property. We prove that the elements of Hutchinson orbits possess the doubling property except perhaps for radii which decrease to zero as the step of the iteration grows, and in this sense, we say that the doubling property of the limit is achieved gradually. We use this result to prove the uniform upper doubling property of the orbits.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Quotient algebraic structures on the set of fuzzy numbers

Creator:
Fechete, Dorina and Fechete, Ioan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
fuzzy number, function with bounded variation, semigroup (monoid) with involution, topological group, and metric space
Language:
English
Description:
A. M. Bica has constructed in \cite{Bica 2007} two isomorphic Abelian groups, defined on quotient sets of the set of those unimodal fuzzy numbers which have strictly monotone and continuous sides. In this paper, we extend the results of above mentioned paper, to a larger class of fuzzy numbers, by adding the flat fuzzy numbers. Furthermore, we add the topological structure and we characterize the constructed quotient groups, by using the set of the continuous functions with bounded variation, defined on [0,1].
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. SOM in metric space

Creator:
Kukal, Jaromír
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
SOM, metric space, batch learning, penalty minimization, and Matlab
Language:
English
Description:
The Self Organized Mapping (SOM) is a kind of artificial neural network (ANN) which enables the pattern set self-organization in space with Euclidean metrics. Thus, the traditional SOM consists of two layers; input one with n nodes and output one with H ones. Every output node is characterized by its weight vector Wk G in this case. The absence of pattern coordinates in special cases is a good motivation for self-organization in any metric space (U, d). The learning in the metric space is introduced on the cluster analysis problém and a basic clustering algorithm is obtained. The relationship with the traditional ISODATA method and NP-completeness is proven. The direct generalization comes to SOM learning in the metric space, its algorithm, properties and NP-completeness. The SOM learning is based on an objective function and its batch minimization. Three estimates of the proposed objective function are included. They will help to study the relationship with Kohonen batch learning, the cluster analysis and the convex programming task. The Matlab source code for the SOM in the metric space is available in the appendix. Two numeric examples are oriented at self-organization in the metric space of written words and the metric space of functions.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public