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Integrability and L₁-convergence of Certain Cosine Sums with Quasi Hyper Convex Coefficients

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In this paper criterion for L1-convergence of a certain cosine sums with quasihyper-convex coefficients is obtained.

Abstract

In this paper criterion for L1-convergence of a certain cosine sums with quasihyper-convex coefficients is obtained.

참고문헌 (14)

  1. R. Bala, "Trigonometric series with semi-convex coefficients", Tamkang J. Math., 18(2), pp.11~17 (1987)
  2. K. N. Bary, "Trigonometric series" (1961), Moscow
  3. L. S. Bosanquet, "Note on convergence and summability factors III", Proc. London Math. Soc., 50, pp.482~496 (1949)
  4. N. L. Braha, "On L₁-convergence of certain cosine sums", Bull. Math. Anal. Appl., 1(1), pp.55~61 (2009)
  5. J. W. Garrett, "On integrability and L1- convergence of certain cosine sums", Notices, Amer. Math. Soc., 22(A-166) (1975)
  6. J. W. Garrett, "On L₁- convergence of certain cosine sums", Proc. Amer. Math. Soc., 54, pp.101~105 (1976)
  7. A. N. Kolmogorov, "Sur l’ordere de grandeur des coefficients de la series de Fourier-Lebesque", Bull. Polon. Sci. Ser. Sci. Math. Astronom. Phys., pp.83~86 (1923)
  8. Kulwinder Kaur, "On L₁- convergence of modified sine sums", An electronic journal of Geography and Mathematics, 14(1), pp.1~6 (2003)
  9. Kulwinder Kaur, "and L1-convergence of Rees-Stanojevic sums with generalized semiconvex coefficients", Int. J. Math. Math. Sci., 30(11), pp.645~650 (2002)
  10. Kumari Suresh, "L₁-convergence of a modified cosine sum.", Indian J. Pure Appl. Math., 19(11), pp.1101~1104 (1988)
  11. B. Ram, "Convergence of certain cosine sums in the metric space L", Proc. Amer. Math.Soc., 66, pp.258~260 (1977)
  12. N. Singh, "Convergence of certain cosine sums in the metric space L", Proc. Amer. Math.Soc, 75, pp.117~120 (1978)
  13. W. H. Young, "On the Fourier series of bounded functions", Proc.London Math. Soc, 12(2), pp.41~70 (1913)
  14. A. Zygmund, "Trigonometric series, Vol. 1" (1959), Cambridge University Press

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