Optimal oral drug dosing via application of the contraction mapping theorem
نویسندگان
چکیده
منابع مشابه
The Contraction Mapping Theorem
A mapping f : X → X from a set X to itself has a fixed point if there is an x ∈ X such that f(x) = x. The simplest fixed point theorem is that a continuous function f : [a, b] → [a, b] has at least one fixed point. This is a consequence of the intermediate value theorem from calculus, as follows. Since f(a) ≥ a and f(b) ≤ b, we have f(b) − b ≤ 0 ≤ f(a) − a. The difference f(x)−x is continuous, ...
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The submartingale convergence theorem is often described as a stochastic analogue to the bounded convergence theorem for monotone sequences of real numbers. We define an alternative process which is a stochastic analogue to an iterative contraction process. A general convergence theorem is presented, with an extension to multivariate processes. The convergence theorem functions in a manner simi...
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denote the open ball of radius a centred on the origin in IR. If the function ~g : Ba → IR d obeys there is a constant G < 1 such that ‖~g(~x)− ~g(~y)‖ ≤ G ‖~x− ~y‖ for all ~x, ~y ∈ Ba (H1) ‖~g(~0)‖ < (1−G)a (H2) then the equation ~x = ~g(~x) has exactly one solution. Discussion of hypothesis (H1): Hypothesis (H1) is responsible for the word “Contraction” in the name of the theorem. Because G <...
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1. Horton WA, Hecht JT. Disorders for which defects are poorly understood or unknown. In: Nelson Textbook of Pediatrics, 20th edn. Eds. Kliegman RM, Stanton BF, St. Gema JW, Schor NF, Behrman RE. Philadelphia: WB Saunders Co, 2011. p.3379. 2. Krishnamurthy S, Srinivasan S. Severe thrombocytosis as initial manifestation of Caffey disease in a 4 month old infant. Pediatr Blood Cancer. 2012;59:345...
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ژورنال
عنوان ژورنال: Biomedical Signal Processing and Control
سال: 2011
ISSN: 1746-8094
DOI: 10.1016/j.bspc.2010.06.006