On approximation of functions, conjugate to the functions of several variables belonging to weighted Lipschitz and Zygmund classes

Year 2024, Early Access, 1 - 18

Shailesh Kumar Srivastava , Sachin Devaiya

https://doi.org/10.15672/hujms.1318033

Abstract

In the present paper, we introduce a new weighted Lipschitz class W(Lp(TN), ξ1(s1), . . . , ξN(sN)) and Zygmund class Z(Lp(TN), ξ1(s1), . . . , ξN(sN)) for N ∈ N, which generalizes the classes given in [7, 11]. We prove two theorems about
the degree (error) of approximation of functions, conjugate to the N-variable functions (2π-periodic in each variable) belonging to these classes using the N-multiple matrix means of their N-multiple conjugate Fourier series. We improve the results of Móricz and Rhoades [6] and Móricz and Shi [7], which are given in the form of corollaries.

Keywords

Degree (error) of approximation, Weighted Lipschitz class, Weighted Zygmund class, N-multiple matrix means

Project Number

Award No.: 09/1007(0008)/2020-EMR-I; Grant No. 2020- 21/Seed Money/26

Thanks

This work was supported by the Council of Scientific and Industrial Research (CSIR), New Delhi, India [Award No.: 09/1007(0008)/2020-EMR-I], and Sardar Vallabhbhai National Institute of Technology, Surat-395007, Gujarat [Grant No. 2020- 21/Seed Money/26].

References

• [1] Deepmala, L.N. Mishra and V.N. Mishra,Trigonometric approximation of signals (functions) belonging to the W(Lr, ξ(t)),(r ≥ 1)−class by (E, q)(q > 0)-means of the conjugate series of its Fourier series, Glob. J. Math. Sci. 2 (2), 6169, 2014