scholarly journals A new class of numerical sequences and its applications to uniform convergence of sine series

2011 ◽  
Vol 284 (14-15) ◽  
pp. 1985-2002 ◽  
Author(s):  
Bogdan Szal
Keyword(s):  
Uniform Convergence ◽  
Sine Series ◽  
New Class

scholarly journals Uniform Convergence of Cosine Series With Coefficient from New Class of General Monotone

2019 ◽  
Vol 1 (2) ◽  
pp. 38-42
Author(s):  
Moch Aruman Imron
Keyword(s):  
Uniform Convergence ◽  
Sine Series ◽  
Negative Sequence ◽  
Cosine Series ◽  
New Class ◽  
Series Coefficient ◽  
Monotone Sequences ◽  
The Difference

General monotone sequences class (GMS) has been introduced by Tikhonov. Then Bogdan Szal extended this class to the new class called new class of general monotone. By using non-negative sequence is called 𝛽 to controle the difference of sine series coefficient. By substituting 𝛽 of modulus of sine series coefficient, we study uniform convergence of new class of general monotone on cosine series.

scholarly journals On the uniform convergence of double sine series

2009 ◽  
Vol 193 (1) ◽  
pp. 79-97 ◽  
Author(s):  
Péter Kórus ◽  
Ferenc Móricz
Keyword(s):  
Uniform Convergence ◽  
Sine Series

scholarly journals On the Uniform Convergence of Sine Series with Square Root

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Sergiusz Kęska
Keyword(s):  
Uniform Convergence ◽  
Real Sequence ◽  
Sufficient Condition ◽  
Square Root ◽  
Necessary And Sufficient Condition ◽  
Sine Series ◽  
Convergence Of Series ◽  
Necessary And Sufficient

Chaundy and Jolliffe proved that if {ck}k=1∞ is a nonincreasing real sequence with limk→∞ck=0, then the series ∑k=1∞‍cksin⁡kx converges uniformly if and only if kck→0. The purpose of this paper is to show that kck→0 is a necessary and sufficient condition for the uniform convergence of series ∑k=1∞‍cksin⁡kθ in θ∈[0,π]. However for ∑k=1∞‍cksin⁡k2θ it is not true in θ∈[0,π].

scholarly journals On the uniform convergence of double sine series

2018 ◽  
Vol 151 (1) ◽  
pp. 71-95 ◽  
Author(s):  
Krzysztof Duzinkiewicz ◽  
Bogdan Szal
Keyword(s):  
Uniform Convergence ◽  
Sine Series
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