STUDY OF ERROR OF APPROXIMATION OF

CONJUGATE FOURIER SERIES IN WEIGHTED

CLASS BY ALMOST RIESZ MEANS

CONJUGATE FOURIER SERIES IN WEIGHTED

CLASS BY ALMOST RIESZ MEANS

Kusum Sharma

Department of Mathematics

National Institute of Technology

Uttarakhand – 246174, INDIA

Department of Mathematics

National Institute of Technology

Uttarakhand – 246174, INDIA

Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

- [1] A. Zygmund, Trigonometric Series, Cambridge University Press, London (1968).
- [2] E.Z. Psarakis and G.V. Moustakides, An L2-based method for the design of 1-D zero phase FIR digital filters, IEEE Trans. Circuit and Sys. I: Fund. The. and Appl., 44, No 7 (1997), 591-601.
- [3] G.G. Lorentz, A contribution to the theory of divergent series, Acta. Math., 80 (1948), 167-190.
- [4] G.M. Petersen, Regular Matrix Transformations, Mc. Hill Publishing Company Ltd., London (1966).
- [5] H.H. Khan, On the degree of approximation to a function to weighted W(Lp, (t))-class, Aligarh Bull. Math., 3/4 (1973-1974), 83-88.
- [6] H.K. Nigam and K. Sharma, Degree of approximation of a class of function by (C, 1)(E, q) means of Fourier series, IAENG Int. J. Appl. Math., 4, No 2 (2011), 1-5.
- [7] H.K. Nigam and K. Sharma, Degree of approximation of a function belonging to Lip((t), r) class by (E1)(C, 1) product means, Int. J. Pure Appl. Math., 70, No 6 (2011), 775-784.
- [8] J.P. King, Almost summable sequences, Proc. Amer. Math. Soc., 17 (1966), 120-125.
- [9] K. Qureshi, On the degree of approximation of a periodic function f by almost Riesz means of its conjugate series, Indian J. Pure Appl. Math., 13, No 10 (1982), 1136-1139.
- [10] K. Sharma and S.S. Malik, A study on degree of approximation of a function belonging to weighted class by product summability of Fourier series, AIP Conf. Proceedings, 2142 (2019), # 170010; doi: 10.1063/1.5122607.
- [11] K. Sharma, Estimation of error of approximation in Lip((t), r) class by (Np q .C1) transform, IAENG Int. J. of Applied Mathematics, 50, No 2 (2020), 251-255.
- [12] L. McFadden, Absolute N¨orlund summability, Duke Math. J., 9 (1942), 168-207.
- [13] M.L. Mittal, B.E. Rhoades, Degree of approximation of functions in the Holder metric, Radovi Mat., 10 (2001), 61–75.
- [14] M.L. Mittal and V.N. Mishra, Approximation of signals (functions) belonging to the weighted W(Lp, (t))-class by almost matrix summability method of its Fourier series, J. Math. Sci. and Eng. Appl. (IJMSEA), 2 (2008), 285-294.
- [15] N.K. Sharma and R. Sinha, On the degree of approximation of a periodic function f by almost Riesz means of its conjugate series, Commun. Fac. Sci. Univ. Ank. Ser. A, 41 (1992), 111-117.
- [16] P.I. Sharma and K. Qureshi, On the degree of approximation of the periodic function f by almost Riesz means, Ranchi University J., 11 (1980), 29-43.
- [17] R.N. Mohapatra, Functions of class Lip(, p) and their Taylor mean, J. Appr. Theory, 45, No 4 (1985), 363-374.
- [18] S. Nanda, Some sequence spaces and almost convergence, J. Austral. Math. Soc. Ser. A, 22 (1976), 446-455.
- [19] Z.U. Ahmad and M. Mursaleen, An application of Banach limits, Proc. Amer. Math. Soc., 103, No 1 (1988), 244-246.