Degree of approximation of a function belonging to weighted $(L_r ,\xi(t ))$ class by (C,1)(E,q) means

Authors

  • Hare Krishna Nigam Department of Mathematics, Faculty of Engineering and Technology, Mody Institute of Technology and Science(Deemed University), Lachhmangarh, Sikar, Rajasthan-332311(India)

DOI:

https://doi.org/10.5556/j.tkjm.42.2011.514

Keywords:

Degree of approximation, class of functions, (C, 1) summability, (E, q) summability, 1)(E, q) product summability, Fourier series, Lebesgue integral.

Abstract

In this paper, a new theorem on degree of approximation of a function class by (C,1)(E,q) product summability means of Fourier series has been proved.

Author Biography

Hare Krishna Nigam, Department of Mathematics, Faculty of Engineering and Technology, Mody Institute of Technology and Science(Deemed University), Lachhmangarh, Sikar, Rajasthan-332311(India)

Department of Mathematics

Assistant Professor

References

G. Alexits, Convergence Problems of Orthogonal Series, Pergamon Press, London, 1961.

PremChandra, Trigonometric approximationof functions in Lp norm, J.Math. Anal. Appl., 275 (2002), 13–26.

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

H. H. Khan, On degree of approximation of functions belonging to the class Lip$(alpha,p)$, Indian J. Pure Appl.

Math. 5 (1974), 132–136.

László Leindler, Trigonometric approximation of functions in Lp norm, J.Math. Anal. Appl. 302 (2005).

LeonardMcFadden, Absolute Nörlund summability, DukeMath. J., 9 (1942), 168–207.

K. Qureshi, On the degree of approximation of a periodic function f by almost Nörlund means, Tamkang J.

Math., 12 (1981), 35–38.

K. Qureshi, On the degree of approximation of a function belonging to the class $text{Lip}_alpha$, Indian J. pure Appl. Math., 13 (1982), 898–903.

K. Qureshi, On the degree of approximation of a function belonging to weighted W$(L_r ,xi(t ))$ class, Indian J. pure Appl.Math., 13 (1982), 471–475.

K. Qureshi and H. K. Neha, A class of functions and their degree of approximation, Ganita., 41 (1990), 37–42.

B. E. Rhaodes, On the degree of approximation of functions belonging to Lipschitz class by Hausdorff means of its Fourier series, Tamkang J.Math., 34 (2003), 245 -247.

B. N. Sahney and D. S. Goel, On the degree of continuous functions, Ranchi University, Math. Jour., 4 (1973), 50–53.

E. C. Titchmarsh, The Theory of functions,Oxford University Press, 1939, 402–403.

A. Zygmund, Trigonometric Series, 2nd rev. ed., Vol. 1, Cambridge Univ. Press, 1959.

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Published

2011-03-22

How to Cite

Nigam, H. K. (2011). Degree of approximation of a function belonging to weighted $(L_r ,\xi(t ))$ class by (C,1)(E,q) means. Tamkang Journal of Mathematics, 42(1), 31–37. https://doi.org/10.5556/j.tkjm.42.2011.514

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Papers