ON THE $||T||\cdot C_1$ SUMMABILITY OF A SEQUENCE OF FOURIER COEFFICIENTS

Authors

  • M. L. MITTAL Department of Mathematics, University of Roorkee, Roorkee-247 667, India.
  • G. PRASAD Department of Mathematics, University of Roorkee, Roorkee-247 667, India.
  • RAJESH KUMAR Department of Mathematics, University of Roorkee, Roorkee-247 667, India.

DOI:

https://doi.org/10.5556/j.tkjm.22.1991.4566

Keywords:

summability, sequence of Fourier coefficients

Abstract

Mohanty and Nanda (1959) were the first to establish a result for the $(C,1)$ i.e. $C_1$-summability of the sequence $\{n B_n(x)\}$. Varshney (1959) improved the result for $(N, \frac{1}{n+1} ) \cdot C_1$  summability which was generalised by several investiga- tors such as Sharma (1970), Singh (1963), Lal (1971), Khare and Singh (1988) etc. In this note, we have·discussed $||T||\cdot C_1$-summability of the sequence $\{n B_x(x)\}$ which includes the result due to Khare and Singh (1988).

References

S. P. Khare and M. Singh, "A study of the sequence of Fourier Coefficients", Bull. Cal. Math. Soc. 80, (1988) 161.

S. N. Lal, "On the Norlund Summability of Fourier Series and the behaviour of Fourier Coefficient", Indian JI. Math. 13, (1971) 177.

R. Mohanty and M. Nanda, "On the behaviour of Fourier Coefficients", Proc. Amer. Math. Soc. 5, (1954) 79.

R. M. Sharma, "On (N,Pn).Ci summability of the sequence {nBn(x)}", Rend. Gire. Palermo 2, 19, (1970) 217.

O. P. Varshney, "On a sequence of Fourier Coefficients", Proc. Amer. Math. Soc. 10, (1959) 790.

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Published

1991-03-01

How to Cite

MITTAL, M. L., PRASAD, G., & KUMAR, R. (1991). ON THE $||T||\cdot C_1$ SUMMABILITY OF A SEQUENCE OF FOURIER COEFFICIENTS. Tamkang Journal of Mathematics, 22(1), 25–29. https://doi.org/10.5556/j.tkjm.22.1991.4566

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