Summability of Fourier Series and its Derived Series by Matrix Means

Abstract

This Paper introduces the concept of matrix operators and establishes two new theorems on matrix summability of Fourier series and its derived series. the results obtained in the paper further extend several known results on linear operators. Various types of criteria, under varying conditions, for the matrix summability of the Fourier series, In this paper quite a different and general type of criterion for summability of the Fourier Series has been obtained, in the theorem function  is integrable in the sense of Lebesgue to the interval [-\pi,\pi] and period with period 2\pi.

Keywords

• Summability,matrix summability,Fourier series,derived Fourier series

References

1. [1] B. P. Padhy, B. Mallik, U. K. Misra and M. Misrapaikray and U. Misra, On product summability of Fourier series using 3, (2016), 191-195.
2. [2] A. Alotibi, M. Mursaleen, Applications of Hankel and regular metrices in Fourier series, (2013), 1-3.
3. [3] H. K. Nigam, K. Sharma, On double dummability of double conjugate Fourier series 2012, (2012), 1-15.
4. [4] S. Lal, P. Yadav, Matrix summability of the conjugate series of derived Fourier series 33, (2002), 35-43.
5. [5] S. Lal, on the degree of approximation of conjugate of a function belonging to weighted class by matrix summability means of conjugate series of a fourier series 31, (2000), 279-288.
6. [6] A. Zygmund Trigonometric Series, vol I, Cambridge University Press, Cambridge 1, 2, (1959), 74-124.
7. [7] G. H. Hardi, Divergent Series, Oxford at the Clarendon Press, (1949), 65-66.