On the |K λ|-summability of Fourier series and its conjugate series

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• 作者：Sanghamitra Beuria ; G. Das ; B. K. Ray
• 关键词：42A28
• 刊名：Arabian Journal of Mathematics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：5
• 期：1
• 页码：35-50
• 全文大小：638 KB
• 参考文献：1.Chandra P.: On the absolute Riesz summability of a Fourier series and its application to the absolute convergence of Fourier series. J. Lond. Math. Soc. 4(2), 611–617 (1972)CrossRef
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  3.Kogbetliantz E.: Sur les series absolument sommables par le methode des moyennes arithmetique. Bull. des. Sc Math. 49(2), 234–256 (1925)
  4.Lal S.: On K λ summability of conjugate series of Fourier series. Bull. Calcutta Math. Soc. 89, 97–104 (1997)
  5.Lototsky, A.V.: On a linear transformation of sequences and series. Ivanov. Gos. Ped. Inst. Uc. Zap. Fiz-Mat. Nauki 4, 61–91 (1953, Russian)
  6.Mohanty R.: A criterion for the absolute convergence of Fourier series. Proc. Lond. Math. Soc. 51(2), 186–196 (1949)CrossRef
  7.Mohanty R.: On the absolute Riesz summability of Fourier series and allied series. Proc. Lond. Math. Soc. 52(2), 295–320 (1951)
  8.Polya, G.; Szegö, G.: Problems and Theorems in Analysis, vol. I. Springer International Student Edition. Narosa Publishing House, New Delhi (1979)
  9.Sadangi, P.: Some aspects of approximation theory. Ph.D. Thesis, Utkal University, Bhubaneswar, Orissa, India (2006)
  10.Vučković V.: The summability of Fourier series by Karamata methods. Math. Zeitschr. 89, 192–195 (1965)CrossRef
  
• 作者单位：Sanghamitra Beuria (1)
  G. Das (2)
  B. K. Ray (3)
  
  1. Department of Mathematics, College of Basic Science and Humanities, OUAT, Bhubaneswar, Orissa, India
  2. Institute of Mathematics and Applications, Andharua, Bhubaneswar, 751003, Orissa, India
  3. Plot.No-102, Saheed Nagar, Bhubaneswar, 751007, Orissa, India
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：2193-5351

文摘

The K λ-means were first introduced by Karamata. Vučković first studied the K λ-summability of a Fourier series and later on Lal studied the K λ-summability of a conjugate series. In the present paper, we have studied the |K λ|-summability of Fourier series and conjugate series. Mathematics Subject Classification 42A28