Approximation of functions belonging to the generalized Lipschitz class by $C^{1}\cdot N_{p}$ summability method of conjugate series of Fourier series

Authors

  • Vishnu Narayan Mishra Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Road, Surat-395 007 (Gujarat), India Author
  • Kejal Khatri Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Road, Surat-395 007 (Gujarat), India Author
  • Lakshmi Narayan Mishra L. 1627 Awadh Puri Colony Beniganj, Phase - III, Opp. I.T.I. Ayodhya Main Road, Faizabad - 224 001 (Uttar Pradesh), India Author

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

Subjects:

40G05, 42B05, 42B08

Abstract

In the present study, a new theorem on the degree ofapproximation of function $\tilde{f}$, conjugate to a periodicfunction $f$ belonging to weighted $W(L_r,\xi(t))$-class usingsemi-monotonicity on the generating sequence $\{p_n\}$ has been established.

Downloads

Published

2014-04-15

Issue

Vol. 66 No. 2 (2014): Vol. 66, Issue 2

Section

Articles

License

Copyright (c) 2014 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.