Summability of Fourier Series and its Derived Series by Matrix Means

Year 2019, Issue: 26, 54 - 63, 01.01.2019

Abdelhadi Mohammad Karazon Mohammad Mahmoud Amer

https://izlik.org/JA24CX33FM

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] 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] A. Alotibi, M. Mursaleen, Applications of Hankel and regular metrices in Fourier series, (2013), 1-3.
• [3] H. K. Nigam, K. Sharma, On double dummability of double conjugate Fourier series 2012, (2012), 1-15.
• [4] S. Lal, P. Yadav, Matrix summability of the conjugate series of derived Fourier series 33, (2002), 35-43.
• [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] A. Zygmund Trigonometric Series, vol I, Cambridge University Press, Cambridge 1, 2, (1959), 74-124.
• [7] G. H. Hardi, Divergent Series, Oxford at the Clarendon Press, (1949), 65-66.