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Degree of approximation of functions conjugate to the functions belonging to Lip((𝜉1,𝜉2)𝑟)-class through double Nörlund means

  • Shailesh Kumar Srivastava ORCID logo EMAIL logo , Shivani Luhar ORCID logo and Sachin Devaiya ORCID logo
Published/Copyright: August 6, 2024

Abstract

In this paper, we determine the error of approximation of functions, conjugate to the functions of two variables ( 2 π -periodic in both variables) belonging to the Lipschitz class Lip ( ( ξ 1 , ξ 2 ) ; r ) ( r 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.

MSC 2020: 26A16; 40C05; 41A25

Funding statement: This work was supported by the Sardar Vallabhbhai National Institute of Technology, Surat-395007, Gujarat (Grant No. 2020-21/Seed Money/26).

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Received: 2024-03-27
Revised: 2024-06-17
Accepted: 2024-07-19
Published Online: 2024-08-06

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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