Degree of approximation of functions conjugate to the functions belonging to Lip((𝜉 <sub>1</sub> ,𝜉 <sub>2</sub> )𝑟)-class through double Nörlund means
Abstract In this paper, we determine the error of approximation of functions, conjugate to the functions of two variables ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>2</m:mn> <m:mo></m:mo> <m:mi>π</m:mi> </m:mrow> </m:math> 2\pi -periodic in both variables) belonging to the Lipschitz class <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>Lip</m:mi> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:msub> <m:mi>ξ</m:mi> <m:mn>1</m:mn> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mi>ξ</m:mi> <m:mn>2</m:mn> </m:msub> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>;</m:mo> <m:mi>r</m:mi> </m:mrow> </m:mrow> </m:math> \operatorname{Lip}((\xi_{1},\xi_{2});r ) ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>r</m:mi> <m:mo>≥</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> r\geq 1 ), through the double Nörlund means of its conjugate double Fourier series. Additionally, in the form of corollaries, we present some particular cases of the theorem proved here.
Authors
- Sachin Devaiya (ORCID: https://orcid.org/0000-0002-3470-9400)
- Shailesh Kumar Srivastava (ORCID: https://orcid.org/0000-0002-6039-5839)
- Shivani Luhar
Institutions
- Sardar Vallabhbhai National Institute of Technology Surat (IN)
Publication Details
- Journal
- Journal of Applied Analysis
- Published
- 2024-08-05
- DOI
- https://doi.org/10.1515/jaa-2024-0048
- Primary Topic
- Approximation Theory and Sequence Spaces
- Type
- article
- Field-Weighted Citation Impact
- 0.00