Results 1 to 10 of about 87 (65)
Nearly Comonotone Approximation
Journal of Approximation Theory, 1998 Let \(I=[-1,1]\) and for \(s\geq 1\) let \(Y=\{y_i\}_{i=0}^s,- 1 ...
Leviatan, D., Shevchuk, I.A.
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Comonotone approximation with interpolation at the ends on an interval
Analysis in Theory and Applications, 2006 Summary: Let a function \(f\in C[-1,1]\), changes its monotonicity at the finite collection \(Y:= \{y_1,\dots,y_s\}\) of \(s\) points \(y_i\in(-1,1)\). For each \(n\geq N(Y)\), we construct an algebraic polynomial \(P_n\), of degree \(\leq n\), which is comonotone with \(f\), that is changes its monotonicity at the same points \(y_i\) as \(f\), and \[ |
G A Dzyubenko, Dzyubenko G A
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Comonotone approximation and interpolation by entire functions
Journal of Mathematical Analysis and Applications, 2019 A theorem of Hoischen states that given a positive continuous function $\varepsilon:\mathbb{R}\to\mathbb{R}$, an integer $n\geq 0$, and a closed discrete set $E\subseteq\mathbb{R}$, any $C^n$ function $f:\mathbb{R}\to\mathbb{R}$ can be approximated by an entire function $g$ so that for $k=0,\dots,n$, and $x\in\mathbb{R}$, $|D^{k}g(x)-D^{k}f(x)|< ...
Maxim R Burke
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Some Positive Results and Counterexamples in Comonotone Approximation
Journal of Approximation Theory, 1997 For part I see the authors in ibid. 89, No. 2, 195-206 (1997; Zbl 0870.41016).
Leviatan, D., Shevchuk, I.A.
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Monotone and comonotone polynomial approximation revisited
Journal of Approximation Theory, 1988 Let the \(L_ p[-1,1]\) best approximation by nth degree monotone polynomials to a monotone function f be denoted by \(E^*_ n(f)_ p\). The author proves \(E^*_ n(f)_ p\leq C\omega^ 2_{\phi}(f,1/n)_ p,\) where \(\phi (x)=\sqrt{1-x^ 2}\) and \(\omega^ 2_{\phi}(f,t)_ p=\sup_ ...
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Quantitative approximation by nonlinear Angheluta-Choquet singular integrals
Journal of Numerical Analysis and Approximation Theory, 2020 By using the concept of nonlinear Choquet integral with respect to a capacity and as a generalization of the Poisson-Cauchy-Choquet operators, we introduce the nonlinear Angheluta-Choquet singular integrals with respect to a family of submodular set ...
Sorin Gal, Ionut Iancu
doaj +7 more sources
Comonotone polynomial approximation
Journal of Approximation Theory, 1974 Eli Passow +2 more
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Best comonotone approximation [PDF]
Transactions of the American Mathematical Society, 1994 The authors have described a general theory of best comonotone approximation in \(C[a,b]\) by elements of an \(n\)-dimensional extended Chebyshev subspace. Two theorems on characterizations are studied which seem to be useful for the actual computation of best comonotone approximations.
Deutsch, Frank, Zhong, Jun
openaire +1 more source
Comonotonic approximations for optimal portfolio selection problems [PDF]
Journal of Risk and Insurance, 2004 We investigate multiperiod portfolio selection problems in a Black & Scholes type market where a basket of 1 riskless and m risky securities are traded continuously. We look for the optimal allocation of wealth within the class of 'constant mix' portfolios.
Dhaene, Jan +4 more
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Comonotone approximation by splines of piecewise monotone functions
Journal of Approximation Theory, 1982 Leviatan, D, Mhaskar, H.N
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