holder classes
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2021 ◽  
pp. 1-26
Author(s):  
Eero Saksman ◽  
Odí Soler i Gibert


Author(s):  
Dmitriy A. Pavlov ◽  

We give a constructive description of Hölder classes of functions on certain compacts in Rm (m > 3) in terms of a rate of approximation by harmonic functions in shrinking neighborhoods of these compacts. The considered compacts are a generalization to the higher dimensions of compacts that are subsets of a chord-arc curve in R3. The size of the neighborhood is directly related to the rate of approximation it shrinks when the approximation becomes more accurate. In addition to being harmonic in the neighborhood of the compact the approximation functions have a property that looks similar to Hölder condition. It consists in the fact that the difference in values at two points is estimated in terms of the size of the neighborhood, if the distance between these points is commensurate with the size of the neighborhood (and therefore it is estimated in terms of the distance between the points).



Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2034
Author(s):  
Mohammad Hasan Abdul Sathar ◽  
Ahmad Fadly Nurullah Rasedee ◽  
Anvarjon A. Ahmedov ◽  
Norfifah Bachok

The current study proposes a numerical method which solves nonlinear Fredholm and Volterra integral of the second kind using a combination of a Newton–Kantorovich and Haar wavelet. Error analysis for the Holder classes was established to ensure convergence of the Haar wavelets. Numerical examples will illustrate the accuracy and simplicity of Newton–Kantorovich and Haar wavelets. Numerical results of the current method were then compared with previous well-established methods.



2020 ◽  
Vol 60 ◽  
pp. 101497
Author(s):  
Paweł M. Morkisz ◽  
Leszek Plaskota


2020 ◽  
Vol 10 (2) ◽  
pp. 35-40
Author(s):  
Tulkin Mamatov ◽  
Rano Sabirova ◽  
Zilola Hamraeva


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