scholarly journals Pringsheim Convergence and the Dirichlet Function

2016 ◽  
Vol 06 (06) ◽  
pp. 441-445
Author(s):  
Thomas Beatty ◽  
Bradley Hansen
Keyword(s):  
Pringsheim Convergence

Pringsheim convergence of double sequences for uniform boundedness principle

2017 ◽  
Vol 10 (04) ◽  
pp. 1750080
Author(s):  
C. Ganesa Moorthy ◽  
C. T. Ramasamy
Keyword(s):  
Uniform Boundedness ◽  
Double Sequences ◽  
Pringsheim Convergence ◽  
Directed Set ◽  
Uniform Boundedness Principle ◽  
Positive Integers

The set of all pairs of positive integers is considered as a directed set under the direction: [Formula: see text] if and only if [Formula: see text] and [Formula: see text]. This directed set is used for Pringsheim-type convergence of double sequences. Consequences of uniform boundedness principle through double sequences are derived in this paper.

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