On trigonometric approximation of W(Lp,ξ(t)) (p≥1) function by product (C,1)(E,1) means of its Fourier series

In the present paper, we generalize a theorem of Lal and Singh (Indian J. Pure Appl. Math. 33(9):1443-1449, 2002) on the degree of approximation of a function belonging to the weighted W ( L p , ξ ( t ) ) ( p ≥ 1 )-class using product ( C , 1 ) ( E , 1 ) means of its Fourier series. We have used her...

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Bibliographic Details
Published in:Journal of inequalities and applications 2013-06, Vol.2013 (1), p.300-300, Article 300
Main Authors: Mishra, Vishnu Narayan, Sonavane, Vaishali, Mishra, Lakshmi Narayan
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Mathematics
Mathematics and Statistics
Proceedings of the International Congress in Honour of Professor Hari M. Srivastava
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Summary:In the present paper, we generalize a theorem of Lal and Singh (Indian J. Pure Appl. Math. 33(9):1443-1449, 2002) on the degree of approximation of a function belonging to the weighted W ( L p , ξ ( t ) ) ( p ≥ 1 )-class using product ( C , 1 ) ( E , 1 ) means of its Fourier series. We have used here the modified definition of the weighted W ( L p , ξ ( t ) ) ( p ≥ 1 )-class of functions in view of Khan (Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 31:123-127, 1982) and rectified some errors appearing in the paper of Lal and Singh (Indian J. Pure Appl. Math. 33(9):1443-1449, 2002). A few applications of approximation of functions will also be highlighted. MSC: 40C99, 40G99, 41A10, 42B05, 42B08.
ISSN:1029-242X
1029-242X
DOI:10.1186/1029-242X-2013-300