Research Article
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Summability of Fourier Series and its Derived Series by Matrix Means

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

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.

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

Abstract

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.
There are 7 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Abdelhadi Mohammad Karazon This is me

Mohammad Mahmoud Amer This is me

Publication Date January 1, 2019
Submission Date May 31, 2018
Published in Issue Year 2019 Issue: 26

Cite

APA Karazon, A. M., & Amer, M. M. (2019). Summability of Fourier Series and its Derived Series by Matrix Means. Journal of New Theory(26), 54-63.
AMA Karazon AM, Amer MM. Summability of Fourier Series and its Derived Series by Matrix Means. JNT. January 2019;(26):54-63.
Chicago Karazon, Abdelhadi Mohammad, and Mohammad Mahmoud Amer. “Summability of Fourier Series and Its Derived Series by Matrix Means”. Journal of New Theory, no. 26 (January 2019): 54-63.
EndNote Karazon AM, Amer MM (January 1, 2019) Summability of Fourier Series and its Derived Series by Matrix Means. Journal of New Theory 26 54–63.
IEEE A. M. Karazon and M. M. Amer, “Summability of Fourier Series and its Derived Series by Matrix Means”, JNT, no. 26, pp. 54–63, January 2019.
ISNAD Karazon, Abdelhadi Mohammad - Amer, Mohammad Mahmoud. “Summability of Fourier Series and Its Derived Series by Matrix Means”. Journal of New Theory 26 (January 2019), 54-63.
JAMA Karazon AM, Amer MM. Summability of Fourier Series and its Derived Series by Matrix Means. JNT. 2019;:54–63.
MLA Karazon, Abdelhadi Mohammad and Mohammad Mahmoud Amer. “Summability of Fourier Series and Its Derived Series by Matrix Means”. Journal of New Theory, no. 26, 2019, pp. 54-63.
Vancouver Karazon AM, Amer MM. Summability of Fourier Series and its Derived Series by Matrix Means. JNT. 2019(26):54-63.


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