Results 21 to 30 of about 90 (88)
Box dimension, oscillation and smoothness in function spaces
Journal of Function Spaces, Volume 3, Issue 3, Page 287-320, 2005., 2005 The aim of this paper is twofold. First we relate upper and lower box dimensions with oscillation spaces, and we develop embeddings or inclusions between oscillation spaces and Besov spaces. Secondly, given a point in the (1p, s)‐plane we determine maximal and minimal values for the upper box dimension (also the maximal value for lower box dimension ...
Abel Carvalho, Hans Triebel
wiley +1 more source
Another extension of Orlicz‐Sobolev spaces to metric spaces
Abstract and Applied Analysis, Volume 2004, Issue 1, Page 1-26, 2004., 2004 We propose another extension of Orlicz‐Sobolev spaces to metric spaces based on the concepts of the Φ‐modulus and Φ‐capacity. The resulting space NΦ1 is a Banach space. The relationship between NΦ1 and MΦ1 (the first extension defined in Aïssaoui (2002)) is studied.
Noureddine Aïssaoui
wiley +1 more source
Arcwise connected attractors of infinite iterated function systems
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 The aim of this paper is to give a sufficient condition for the attractor of an infinite iterated function system to be arcwise connected.
Dumitru Dan
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Self‐similar random fractal measures using contraction method in probabilistic metric spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 52, Page 3299-3313, 2003., 2003 Self‐similar random fractal measures were studied by Hutchinson and Rüschendorf. Working with probability metric in complete metric spaces, they need the first moment condition for the existence and uniqueness of these measures. In this paper, we use contraction method in probabilistic metric spaces to prove the existence and uniqueness of self‐similar
József Kolumbán +2 more
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Weighted Variable Exponent Sobolev spaces on metric measure spaces
Moroccan Journal of Pure and Applied Analysis, 2018 In this article we define the weighted variable exponent-Sobolev spaces on arbitrary metric spaces, with finite diameter and equipped with finite, positive Borel regular outer measure.
Hassib Moulay Cherif, Akdim Youssef
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The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 1, Page 11-21, 2002., 2002 We weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have positive and finite Hausdorff measures, which in certain extent generalize some of the known results ...
Hongwen Guo, Dihe Hu
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Strongly nonlinear potential theory on metric spaces
Abstract and Applied Analysis, Volume 7, Issue 7, Page 357-374, 2002., 2002 We define Orlicz‐Sobolev spaces on an arbitrary metric space with a Borel regular outer measure, and we develop a capacity theory based on these spaces. We study basic properties of capacity and several convergence results. We prove that each Orlicz‐Sobolev function has a quasi‐continuous representative. We give estimates for the capacity of balls when
Noureddine Aïssaoui
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Abstract and Applied AnalysisMSC2020 Classification: 28A80, 47H10, 54E50 ...
A. Herminau Jothy +3 more
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Fractal multiwavelets related to the cantor dyadic group
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 2, Page 307-314, 1998., 1997 Orthogonal wavelets on the Cantor dyadic group are identified with multiwavelets on the real line consisting of piecewise fractal functions. A tree algorithm for analysis using these wavelets is described. Multiwavelet systems with algorithms of similar structure include certain orthogonal compactly supported multiwavelets in the linear double‐knot ...
W. Christopher Lang
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A Unified Framework Linking Entropy, Fractal Dimension, and Lyapunov Exponents in Chaotic Dynamics
Complexity, Volume 2026, Issue 1, 2026.This study presents a universal operator framework predicting critical transitions in nonlinear systems through the intrinsic nexus of entropy, fractal geometry, and chaos. We derive a unified model (Equation 4) that integrates fractal dimension (Dᵓ), Lyapunov exponents (λᵢ), and entropy (S) into a single predictive equation, justified through ...
Elio Quiroga Rodríguez, Naoki Masuda
wiley +1 more source