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Constructive Bounded Sequences and Lipschitz Functions
Author(s) -
Julian William,
Phillips Keith
Publication year - 1985
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-31.3.385
Subject(s) - constructive , lipschitz continuity , bounded function , mathematics , characterization (materials science) , generalization , multiplier (economics) , lipschitz domain , sequence (biology) , pure mathematics , bounded deformation , discrete mathematics , constructive proof , uniform boundedness , mathematical analysis , computer science , process (computing) , materials science , genetics , biology , economics , macroeconomics , nanotechnology , operating system
Multiplier conditions equivalent to the constructive boundedness of a non‐negative real sequence M are derived. If the termwise product sM is bounded in sum whenever s is bounded in sum, then an upper bound for M can be constructed. One consequence is a constructive generalization of Fichtenholz's characterization of Lipschitz functions on metric spaces. The appropriate Lipschitz constants are constructed in the sense of Bishop's constructive mathematics.