Strong Riesz summability of Fourier series

• Jena, Bidu Bhusan ^[1] ; Paikray, Susanta Kumar ^[1] ; Misra, Umakanta ^[2]
  1. [1] Veer Surendra Sai University of Technology

     Veer Surendra Sai University of Technology

     India

     
  2. [2] National Institute of Science and Technology

     National Institute of Science and Technology

     Indonesia

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 6, 2020, págs. 1615-1626
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-06-0096
• Enlaces
  • Texto completo
• Resumen

  • The notion of strong summability was introduced by Fekete (Math. És Termesz Ertesitö, 34 (1916), 759-786). Dealing with Nörlund summability of Fourier series Mittal (J. Math. Anal. Appl. 314 (2006), 75-84) has established a result on strong summability. We have established a new result on sufficient condition for strong Riesz summability of Fourier series.

• Referencias bibliográficas
  • A. A. Das, B. B. Jena, S.K. Paikray and R. K. Jati, “Statistical deferred weighted summability and associated Korovkin-type approximation...
  • M. Fekete, “Vizsagàlatok a Fourier-sorokol”, Mathematikai és Természettudományi Értesít?, vol. 34, pp. 759-786, 1916.
  • G. H. Hardy and J. E. Littlewood, “Sur la série de Fourier d’une fonction a carré sommable”, Comptes Rendus de l'Académie des Sciences...
  • J. M. Hyslop, “Note on the strong summability of series”, Glasgow mathematical journal, vol. 1, no. 1, pp. 16-20, Jan. 1951, doi: 10.1017/S2040618500032883
  • B. B. Jena and S. K. Paikray, “Product of statistical probability convergence and its applications to Korovkin-type theorem”, Miskolc mathematical...
  • B. B. Jena, S. K. Paikray, and H. Dutta, “On various new concepts of statistical convergence for sequences of random variables via deferred...
  • B. B. Jena, Vandana, S. K. Paikray, and U. K. Misra, “On generalized local property of |A; ?|k-summability of factored Fourier series”, International...
  • B. B. Jena, S. K. Paikray, and U. K. Misra, “A Tauberian theorem for double Cesàro summability method”, International journal of mathematics...
  • B. B. Jena, S. K. Paikray, and U. K. Misra, “Inclusion theorems on general convergence and statistical convergence of (L, 1, 1)-summability...
  • B. B. Jena, S. K. Paikray, and U. K. Misra, “Statistical deferred Cesàro summability and its applications to approximation theorems”, Filomat,...
  • B. B. Jena, L. N. Mishra, S. K. Paikray, and U. K. Misra, “Approximation of signals by general matrix summability with effects of Gibbs phenomenon”,...
  • M. L. Mittal, “A Tauberian theorem on strong Nörlund summability”, Journal of Indian Mathematical Society, vol. 44, pp. 369-377, 1980.
  • M. L. Mittal, “On strong Nörlund summability of Fourier series”, Journal of mathematical analysis applications, vol. 314, no. 1, pp. 75-84,...
  • M. L. Mittal and R. Kumar, “A note on strong Nörlund summability”, Journal of mathematical analysis applications, vol. 199, no. 1, pp. 312-322,...
  • P. Parida, S. K. Paikray, H. Dutta, B. B. Jena, and M. Dash, “Tauberian theorems for Cesàro summability of nth sequences”, Filomat, vol. 32,...
  • T. Pradhan, S. K. Paikray, B. B. Jena, and H. Dutta, “Statistical deferred weighted B-summability and its applications to associated approximation...
  • H. M. Srivastava, B. B. Jena, S. K. Paikray, and U. K. Misra, “A certain class of weighted statistical convergence and associated Korovkin...
  • H. M. Srivastava, B. B. Jena, S. K. Paikray, and U. K. Misra, “Generalized equi-statistical convergence of the deferred Nörlund summability...
  • H. M. Srivastava, B. B. Jena, S. K. Paikray, and U. K. Misra, “Deferred weighted A-statistical convergence based upon the (p, q)-Lagrange...
  • S. K. Paikray, B. B. Jena, and U. K. Misra, “Statistical deferred Cesàro summability mean based on (p, q)-integers with application to approximation...
  • A. Zygmund, Trigonometric Series, 2nd ed., vol. 1. Cambridge: Cambridge University Press, 1959.