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The Weighted Discrepancies of Some Slowly Increasing Sequences
Author(s) -
Ohkubo Yukio
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951740117
Subject(s) - mathematics , sequence (biology) , combinatorics , integer (computer science) , upper and lower bounds , inequality , mathematical analysis , genetics , computer science , biology , programming language
In this note we give upper bounds of the weighted discrepancy of the sequence ( f ( n )), when f ″( x ) satisfies some conditions. Furthermore, by applying the generalized van der Corput's inequality, we give upper bounds of the weighted discrepancy of the sequence ( f ( n )), when some conditions about f (q + 2)( x ) is satisfied, where q is any positive integer.
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