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A Markov-type inequality for seminormed fuzzy integrals

Applied Mathematics and Computation, 2013
In this paper, we present a Markov-type inequality for seminormed fuzzy integrals and its connections with Chebyshev's inequality and other fundamental properties of the classical integral.10752107461,1431 ...
J Caballero
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New Inequalities of Markov Type

SIAM Journal on Mathematical Analysis, 1987
For any polynomial f with complex coefficients we define \(\| f\|:=\{\int^{b}_{a}| f(t)|^ 2w(t)dt\}^{1/2},\) where w: (a,b)\(\to R\) is a positive and integrable function with all moments finite. It is well known that there exists a constant \(\gamma_ n\), not depending on f, such that \(\| f'\| \leq \gamma_ n\| f\|\) for all f, deg \(f\leq n\).
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Equivalence of the Local Markov Inequality and a Kolmogorov Type Inequality in the Complex Plane [PDF]

Potential Analysis, 2012
We prove that a compact subset of the complex plane satisfies a local Markov inequality if and only if it satisfies a Kolmogorov type inequality. This result generalizes a theorem established by Bos and Milman in the real case.
Leokadia Białas-Cież, Białas-Cież, Leokadia, Eggink, Raimondo, Raimondo Eggink   +3 more
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Tangential Markov Inequalities on Transcendental Curves

Constructive Approximation, 2003
Let \(M\) be a smooth manifold in \(\mathbb R^d\). We say that \(M\) admits a tangential Markov inequality of exponent \(\ell\) if there is a constant \(C> 0\) such that, for all polynomials \(P\in \mathbb R[x_1,\dots, x_d]\) and points \(a\in M\), \(| D_T P(a)|\leq C(\deg P)^\ell\| P\|_M\). Here \(D_TP\) denotes any (unit) tangential derivative of \(P\
BOS, LEONARD PETER, Brudnyi A., Levenberg N., Totik V.   +3 more
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Probability Inequalities Related to Markov's Theorem

The American Statistician, 2002
A recurrent theme of interest in probability and statistics is to determine the best bounds for two probabilities, Pr(X ≥ r) and Pr(s < X - μ < t), when only the mean μ and the standard deviation σ of a random variable X are known. This article addresses the issue under two circumstances, when X is arbitrary and when X is nonnegative.
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Analogs of Markov's Inequality in Normed Spaces

Mathematical Notes, 2004
The Markov inequality states \[ | P^{(k)}_n(x)| \leq c_{n,k}\| P_n\| _{C([-1,1])}\quad \text{ for } -1\leq x \leq 1, 0\leq k \leq n \] for all polynomials \(P_n(x)\) of degree at most \(n\) in one real variable \(x\). The best constants \(c_{n,k}\) are explicitly known and they are attained for the Chebyshev polynomials \(T_n(x)=\cos(n\cdot \arccos x)\)
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A V. A. Markov type inequality in Lp

Journal of Soviet Mathematics, 1983
It is proved that for any algebraic polynomial P of degree at most n we have for 1 p ≤ + t8, x ≥ 1 the inequality For p ≥1 and x ≥ 1 we construct a polynomial P* of degree n for ...
Podkorytov, A. N., Dyn'kin, E. M.
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An Inequality of the Markov–Bernstein Type for Polynomials

SIAM Journal on Mathematical Analysis, 1983
Let $ - \infty \leq a < b \leq \infty $ and denote by $w:(a,b) \to \mathbb{R}$ a positive and integrable function, with all moments \[ \int_a^b {t^n } w(t)dt\] finite. For any polynomial f with complex coefficients, we write \[ \| f \| = \left\{ {\int_a^b {| {f(t)} |^2 w(t)dt} } \right\}^{{1 / 2}} .\] Then there exists a constant $\gamma _n ...
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Markov's and Bernstein's Inequalities on Disjoint Intervals

Canadian Journal of Mathematics, 1981
In 1889, A. A. Markov proved the following inequality:INEQUALITY 1. (Markov [4]). If pn is any algebraic polynomial of degree at most n thenwhere ‖ ‖A denotes the supremum norm on A.In 1912, S. N. Bernstein establishedINEQUALITY 2. (Bernstein [2]). If pn is any algebraic polynomial of degree at most n thenfor x ∈ (a, b).In this paper we extend these ...
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Reverse Markov inequality

2002
\textit{P. Turán } showed in [Compositio math., Groningen, 7, 89--95 (1939; JFM 65.0324.01)] that for the interval \(I=[-1,1]\) and polynomials \(p\) with all their zeros in \(I\), the reverse Markov inequality in the following from: \(\| p'\| _I\geq {1\over 6}(\text{deg }p)^{1\over 2}\| p\| _x\).
Levenberg, Norman, Poletsky, Evgeny A.
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