Open Access
Subscription Access
Open Access
Subscription Access
Approximation of Functions in H(α; p)-space By Taylor Means
Subscribe/Renew Journal
In 2014, the authors [Mat. Vesnik, 66(1)(2014),46{57], among the other results, obtained the Jackson order: O(n-α) for 0 < α < 1 as the degree of approximation of functions in a subspace of H(α; p), 0 < α ≤ 1, 1 ≤ p ≤ ∞ space. In the present paper, among the other re- sults, we extend the subspace of H(α; p), used earlier by the authors[ibid], to obtain the Jackson order: O(n-α) for 0 < α ≤ 1 and relax the hypothesis imposed upon the functions in H(α; p) space.
Keywords
Generalized Holder metric, Taylor means, Degree of approximation
Subscription
Login to verify subscription
User
Font Size
Information
- P. Chandra, S. S. Thakur and R. Singh, Functions of Lp-space and Taylor means, Mat. Vesnik, 65(1)(2013), 35{45.
- P. Chandra, S. S. Thakur and R. Singh, Functions of class H( ; p) and Taylor means, Mat. Vesnik, 66(1)(2014), 46{57.
- G. Das, T. Ghosh and B. K. Ray, Degree of approximation of functions by their Fourier series in the generalized Holder metric, Proc. Indian Acad. Sci. (Math. Sci.), 106(1996), 139{153.
- C. K. Chui and A. S. B. Holland, On the order of approximation by Euler and Taylor Means, J. Approx. Theory, 39(1983), 24{38.
- R. L. Forbes, Lebesgue constants for regular Taylor summability, Canad. Math. Bull.,8(1965), 797{808.
- A. S. B. Holland, A survey of degree of continuous functions, SIAM Review, 23(3)(1981), 344{379.
- C. L. Miracle, The Gibbs phenomenon for Taylor means and [F; dn] means, Canad. J. Math., 12(1960), 660-673.
- R. N. Mohapatra and Prem Chandra, Holder continuous functions and their Euler, Borel and Taylor means, Math. Chronicle, 11(1982), 81{96.
- R. N. Mohapatra, A. S. B. Holland and B. N. Sahney, Functions of class Lip( ; p) and their Taylor mean, J. Approx. Theory, 45(1985), 363{374.
- S. Pro ssdorf, Zur Konvergenz der Fourier Reihen Holder stetiger Funktionen, Math. Nachr., 69(1975), 7{14.
- A. Zygmund, Trigonometric Series, Vol. I (Second Edition), Cambridge University Press, London/New York, 1968.
Abstract Views: 374
PDF Views: 0