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APPROXIMATION OF MONOTONE FUNCTIONS BY MONOTONE POLYNOMIALS [PDF]

Russian Academy of Sciences. Sbornik Mathematics, 1993
The direct theorem of Nikolskij-type for monotone polynomial approximation of smooth monotone functions is proved. That result is an extension of classic direct theorems in approximation without constraint of A. F. Timan, V. K. Dzyadyk, G. Freud, Yu. A. Brudnyi.
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Monotonicity of partition functions

Mathematika, 1956
Let \(A\) be an arbitrary set of different positive integers (finite or infinite) other than the empty set or the set consisting of the single element unity. Let \(p(n)=p_A(n)\) denote the number of partitions of the integer \(n\) into parts taken from the set \(A\), repetitions being allowed. Let \(k\) be any integer and suppose we define \(p^{(k)}(n)
Paul Erdös, P. T. Bateman
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Estimating monotone functions

Statistics & Probability Letters, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mark G. Low, Yung-Gyung Kang
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Monotonic functions in EC [PDF]

Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation, 2014
To understand how evolutionary algorithms optimize the simple class of monotonic functions, Jansen (FOGA 2007) introduced the partially-ordered evolutionary algorithm (PO-EA) model and analyzed its runtime. The PO-EA is a pessimistic model of the true optimization process, hence performance guarantees for it immediately take over to the true ...
Gaspard Férey, Sylvain Colin, Benjamin Doerr   +2 more
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On Functions That are Monotone on No Interval

The American Mathematical Monthly, 1981
(1981). On Functions that are Monotone on No Interval. The American Mathematical Monthly: Vol. 88, No. 10, pp. 754-755.
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Weakly monotone functions

Journal of Geometric Analysis, 1994
The definition of monotone function in the sense of Lebesgue is extended to the Sobolev spaces \(W^{1,p}\), \(p>n-1\). It is proven that such weakly monotone functions are continuous except in a singular set of \(p\)- capacity zero, that is empty in the case \(p=n\).
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Some Absolutely Monotonic and Completely Monotonic Functions

SIAM Journal on Mathematical Analysis, 1974
The functions $(1 - r)^{ - 2|\lambda |} (1 - 2xr + r^2 )^{ - \lambda } $ are shown to be absolutely monotonic, or equivalently, that their power series have nonnegative coefficients for $ - 1 \leqq x \leqq 1$. One consequence is a simple proof of Kogbetliantz’s theorem on positive Cesaro summability for ultraspherical series, [7].
Harry Pollard, Richard Askey
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Monotone Boolean functions

Russian Mathematical Surveys, 2003
Summary: Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published.
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Stochastic Monotonicity and Monotonicity of the Value Functions

2016
We consider MDPs and CMs with structured state space and arbitrary transition law. We assume that the minimal assumption (MA1) holds. As in Chap. 6 we are looking for conditions under which the value functions are monotone in the initial state s. This is easy for CMs, but requires a thorough treatment of the notion of stochastic monotonicity for MDPs ...
Karl Hinderer, Ulrich Rieder, Michael Stieglitz   +2 more
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Sexual health among adolescent and young adult cancer survivors: A scoping review from the Children's Oncology Group Adolescent and Young Adult Oncology Discipline Committee

Ca-A Cancer Journal for Clinicians, 2021
Brooke Cherven, Sharon L Bober, Kristin Bingen   +2 more
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