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Best approximation of functions in generalized Hölder class
Journal of Inequalities and Applications
|October 27, 2018
Summary
This study introduces novel error estimation for function classes using Fourier Series (FS) and Conjugate Fourier Series (CFS) methods. These findings generalize previous research, offering new insights into approximation theory.
Area of Science:
- Mathematical Analysis
- Approximation Theory
Background:
- Error estimation is crucial for understanding the accuracy of mathematical approximations.
- Previous studies have explored error bounds for function classes using various series expansions.
Purpose of the Study:
- To determine, for the first time, the error estimation of specific function classes using Fourier Series (FS) and Conjugate Fourier Series (CFS) methods.
- To establish a generalized theorem that encompasses and extends prior results in the field.
Main Methods:
- Utilizing the Fourier Series (FS) method for error estimation.
- Employing the Conjugate Fourier Series (CFS) method for error estimation.
- Developing a novel Theorem 2.1 for generalized error bounds.
Main Results:
- The error estimation for the function classes using FS and CFS methods has been successfully determined.
- Theorem 2.1 is presented, providing a generalized framework for error estimation.
- Previous results from Dhakal (2010, 2013) and Kushwaha & Dhakal (2013) are shown to be specific cases of the new theorem.
Conclusions:
- The study successfully established new error estimations for function classes via FS and CFS.
- The developed theorem offers a significant generalization, unifying and extending prior research.
- The findings contribute to the advancement of approximation theory and error analysis.
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