On ideal equal convergence

We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472]. Our definition of ideal equal convergence...

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Bibliographic Details
Published in:Central European journal of mathematics 2014, Vol.12 (6), p.896-910
Main Authors: Filipów, Rafał, Staniszewski, Marcin
Format: Article
Language:English
Subjects:
26A03
40A30
40A35
54A20
Algebra
Convergence
Convergence of a sequence of functions
Equal convergence
Filter
Filter convergence
Geometry
Ideal
Ideal convergence
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
P-ideal
Pointwise convergence
Probability Theory and Stochastic Processes
Research Article
Sigma-uniform convergence
Statistical convergence
Topological Groups
Uniform convergence
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Summary:We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472]. Our definition of ideal equal convergence encompasses two different kinds of ideal equal convergence introduced in [Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177]_and [Filipów R., Szuca P., Three kinds of convergence and the associated I-Baire classes, J. Math. Anal. Appl., 2012, 391(1), 1–9]. We also solve a few problems posed in the paper by Das, Dutta and Pal.
ISSN:1895-1074
2391-5455
1644-3616
2391-5455
DOI:10.2478/s11533-013-0388-4