Degree of Approximation of a Function Belonging to Lip(x (t), r) Class by (E,1)(C,2) Summability Means
Keywords:
42B05, 42B08Abstract
In this paper, we determine the degree of approximation of a function f belonbing to  Lip(x (t), r) , where xi(t) is nonnegative and increasing function of t, by (E,1)(C,2) product operator on Fourier series associated with f.References
G. Alexits, Convergence problems of orthogonal series, Pergamon Press, London, 1961.
Prem Chandra, Trigonometric approximation of functions in p L - norm, J. Math. Anal. Appl. 275(2002), no. 1, (13-26).
G. H. Hardy, Divergent series, first edition, Oxford University Press, 1949, 70.
H. H. Khan, On degree of approximation of functions belonging to the class Lip (a , p), Indian J. Pure Appl. Math. 5(1974), no.2, 132-136.
Lászaló Leindler, , Trigonometric approximation in p L - norm, J. Math. Anal. Appl. 302(2005).
Leonard McFadden, Absolute Noɺɺulund summability, Duke Math. J. 9 (1942), 168-207.
K. Qureshi, : On the degree of approximation of a periodic function f by almost Noɺɺulund means, Tamkang J. Math. 12(1981), no. 1, 35-38.
K. Qureshi, : On the degree of approximation of a function belonging to the class Lipa , Indian J. pure Appl. Math. 13(1982), no. 8, 560-563.
K. Qureshi, and H. K. Neha, A class of functions and their degree of approximation, Ganita, 41(1) (1990) 37.
B.E. Rhodes, On degree of approximation of functions belonging to lipschitz class (2003).
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. pp. 402-403.
A. Zygmund, Trigonometric series, 2nd rev. ed., Vol. 1, Cambridge Univ. Press, Cambridge, 1959.
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