On the uniform convergence of sine, cosine and double sine-cosine series

Krzysztof Duzinkiewicz

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2016)

  • Volume: 36, Issue: 1, page 87-116
  • ISSN: 1509-9407

Abstract

top
In this paper we define new classes of sequences GM(β,r) and DGM(α,β,γ,r). Using these classes we generalize and extend the P. Kórus results concerning the uniform convergence of sine, cosine and double sine-cosine series, respectively.

How to cite

top

Krzysztof Duzinkiewicz. "On the uniform convergence of sine, cosine and double sine-cosine series." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 36.1 (2016): 87-116. <http://eudml.org/doc/286864>.

@article{KrzysztofDuzinkiewicz2016,
abstract = {In this paper we define new classes of sequences GM(β,r) and DGM(α,β,γ,r). Using these classes we generalize and extend the P. Kórus results concerning the uniform convergence of sine, cosine and double sine-cosine series, respectively.},
author = {Krzysztof Duzinkiewicz},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {sine series; cosine series; double sine-cosine series; uniform convergence; generalized monotonicity},
language = {eng},
number = {1},
pages = {87-116},
title = {On the uniform convergence of sine, cosine and double sine-cosine series},
url = {http://eudml.org/doc/286864},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Krzysztof Duzinkiewicz
TI - On the uniform convergence of sine, cosine and double sine-cosine series
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2016
VL - 36
IS - 1
SP - 87
EP - 116
AB - In this paper we define new classes of sequences GM(β,r) and DGM(α,β,γ,r). Using these classes we generalize and extend the P. Kórus results concerning the uniform convergence of sine, cosine and double sine-cosine series, respectively.
LA - eng
KW - sine series; cosine series; double sine-cosine series; uniform convergence; generalized monotonicity
UR - http://eudml.org/doc/286864
ER -

References

top
  1. [1] T.W. Chaundy and A.E. Jolliffe, The uniform convergence of certain class of trigonometrical series, Proc. London Math. Soc. 15 (1916), 214-216. 
  2. [2] K. Duzinkiewicz and B. Szal, On the uniform convergence of double sine series, http://arxiv.org/pdf/1510.06273v1.pdf. 
  3. [3] P. Kórus, Remarks on the uniform and L1-convergence of trigonometric series, Acta Math. Hungar. 128 (2010), 369-380. doi: 10.1007/s10474-010-9217-4 Zbl1240.42015
  4. [4] P. Kórus, On the uniform convergence of double sine series with generalized monotone coefficients, Periodica Math. Hungar. 63 (2011), 205-214. doi: 10.1007/s10998-011-8205-y Zbl1265.42007
  5. [5] P. Kórus, Uniform convergence of double trigonometric series, Mathematica Bohemica 138 (3) (2013), 225-243. Zbl1289.42018
  6. [6] B. Szal, A new class of numerical sequences and its applications to uniform convergence of sine series, Math. Nachr. 284 (14-15) (2011), 1985-2002. 
  7. [7] B. Szal, On L-convergence of trigonometric series, J. Math. Anal. Appl. 373 (2011), 449-463. doi: 10.1016/j.jmaa.2010.08.003 Zbl1204.42010
  8. [8] D.S. Yu and S.P. Zhou, A generalization of monotonicity condition and applications, Acta Math. Hungar. 115 (2007), 247-267. doi: 10.1007/s10474-007-5253-0 Zbl1136.42002
  9. [9] S.P. Zhou, P. Zhou and D.S. Yu, Ultimate generalization to monotonicity for uniform convergence of trigonometric series, Sci. China Math. 53 (7) (2010), 1853-1862. doi: 10.1007/s11425-010-3138-0 Zbl1211.42006
  10. [10] I.E. Žak and A.A. Šneider, Conditions for uniform convergence of double sine series, Izv. Vysš. Učebn. Zaved. Matematika 4 (1966) in Russian, 44-52. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.