Title: On the Behavior near the Origin of a Sine Series with Coefficients of Monotone Type
Author(s): Xhevat Z. Krasniqi
Pages: 36-44
Cite as:
Xhevat Z. Krasniqi, On the Behavior near the Origin of a Sine Series with Coefficients of Monotone Type, Int. J. Anal. Appl., 4 (1) (2014), 36-44.

Abstract


In this paper we have obtained some asymptotic equalities of the sum function of a trigonometric sine series expressed in terms of its special type of coefficients.

Full Text: PDF

 

References


  1. A. Yu. Popov, Estimates for the sums of sine series with monotone coefficients of certain classes, (Russian) Mat. Zametki 74 (2003), no. 6, 877–888; translation in Math. Notes 74 (2003), no. 5-6, 829–840.

  2. B. V. Simonov, On trigonometric series with (k, s)-monotone coefficients in weighted spaces, Izv. Vyssh. Uchebn. Zaved., Mat. 2003, no. 5, 42-54.

  3. R. Salem, D´etermination de l’ordre de grandeur ´a l’origine de certains s´eries trigonometriques, C. R. Acad. Sci. Paris 186 (1928), 1804-1806.

  4. R. Salem, Essais sur les series trigonometriques, Paris, 1940.

  5. S. Aljanci ˇ c, R. Bojani ´ c´ and M. Tomic´, Sur le comportement asymtotique au voisinage de z´ero des s´eries trigonom´etriques de sinus ´a coefficients monotones, Publ. Inst. Math. Acad. Serie Sci., 10 (1956), 101-120.

  6. S. A. Telyakovski˘ı, On the behavior near the origin of the sine series with convex coefficients, Publ. Inst. Math. Nouvelle serie, 58 (72) (1995), 43-50.

  7. Xh. Z. Krasniqi, Certain estimates for double sine series with multiple–monotone coefficients, Acta Math. Acad. Paedagog. Nyh´azi. (N.S.) 27 (2011), no. 2, 233–243.

  8. Xh. Z. Krasniqi, On the behavior near the origin of double sine series with monotone coef- ficients. Math. Bohem. 134 (2009), no. 3, 255–273.

  9. Xh. Z. Krasniqi, Some estimates of r-th derivative of the sums of sine series with monotone coefficients of higher order near the origin. Int. J. Math. Anal. (Ruse) 3 (2009), no. 1-4, 59–69.

  10. Xh. Z. Krasniqi, N. L. Braha, On the behavior of r-derivative near the origin of sine series with convex coefficients. JIPAM. J. Inequal. Pure Appl. Math. 8 (2007), no. 1, Article 22, 6 pp. (electronic).

  11. W. H. Young, On the mode of oscillation of a Fourier series and of its allied series, Proc. London Math. Soc. 12 (1913), 433-452.

  12. N. Bary, Trigonometric series, Moscow, 1961 (in Russian).