| Approximation of functions belonging to the generalized Lipschitz class by $C^{1}\cdot N_{p}$ summability method of conjugate series of Fourier series |
| Vishnu Narayan Mishra, Kejal Khatri and Lakshmi Narayan Mishra |
Abstract In the present study, a new theorem on the degree of approximation of function $\tilde{f}$, conjugate to a periodic function $f$ belonging to weighted $W(L_r,\xi(t))$-class using semi-monotonicity on the generating sequence $\{p_n\}$ has been established.
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Keywords: Generalized Lipschitz $W(L_r,\xi(t))$-class of functions; conjugate Fourier series; degree of approximation; $C^1$ means; $N_p$ means; product summability $C^{1}\cdot N_{p}$ transform. |
MSC: 40G05, 42B05, 42B08 |
Pages: 155$-$164 |
Volume 66 , Issue 2 , 2014 |
