Approximation of functions of class $Lip(\alpha,r), (r\geq1)$ by $(N,p_n)(E,1)$ summability means of Fourier series

Authors

  • Shyam Lal Professor
  • Abhishek Mishra PHD student

DOI:

https://doi.org/10.5556/j.tkjm.45.2014.876

Keywords:

Trigonometric approximation, Fourier series, regular (N, p_n)means, (E, 1) means and (N, p_n)(E, 1) summability means and generalized Minkowski inequality

Abstract

In this paper, two new theorems on degree of approximation of a function $f\in Lip(\alpha,r), \ \ (r \geq 1)$, have been established. A new technique is applied to find the estimate.

Author Biographies

Shyam Lal, Professor

Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi-221005

Abhishek Mishra, PHD student

Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi-221005,

References

P. Chandra, Approximation by Norlund operators, Mat. Vestnik, 38 (1986), 263-269.

G. H. Hardy, Divergent Series, first edition, Oxford Press, p.70, 1949.

H. H. Khan, On degree of approximation of functions belonging to class $Lip(alpha,p)$, Indian J. Pure Appl. Math., 5(1974), no.2, 132-136.

L. McFaddin, Absolute Norlund summability, Duke Math. J., 9(1942), 168-207.

R. N. Mohapatra and D. C. Russell, Some direct and inverse theorems in approximation of functions, J. Austral. Math. Soc. (Ser. A), 34 (1983), 143-154.

K. Qureshi, On degree of approximation of a periodic function by almost Norlund means, Tamkang J. Math., 12(1981),no.1, 35-38.

K. Qureshi, On degree of approximation of functions belonging to the class $Lipalpha$, Indian J. Pure App. Math, 13(1982), no.8, 898-903.

B. N. Sahney and V. Rao, Error bounds in the approximation of functions, Bull. Austral. Math. Soc., 6(1972), 11-18.

E. C. Titchmarsh, The Theory of functions, Second Edition, Oxford University Press, 1939.

A. Zygmund, Trigonometric Series, 2nd rev.ed., I, Cambridge Univ. Press, Cambridge, 1968.

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Published

2014-09-30

How to Cite

Lal, S., & Mishra, A. (2014). Approximation of functions of class $Lip(\alpha,r), (r\geq1)$ by $(N,p_n)(E,1)$ summability means of Fourier series. Tamkang Journal of Mathematics, 45(3), 243-250. https://doi.org/10.5556/j.tkjm.45.2014.876

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