Results 31 to 40 of about 499 (64)

The Degree of Approximation and Converse Theorems with Exponential-Type Weights

, 2018
Let R = (−∞,∞), and let Q ∈ C1(R) : R → [0,∞) be an even function, which is an exponent. We deal with the exponential-type weights w(x) = e−Q(x), x ∈ R.
R. Sakai
semanticscholar   +1 more source

Construction of a class of half-discrete Hilbert-type inequalities in the whole plane

Open Mathematics
In this work, we first define two special sets of real numbers, and then, we construct a half-discrete kernel function where the variables are defined in the whole plane, and the parameters in the kernel function are limited to the newly constructed ...
You Minghui
doaj   +1 more source

Letter to the Editor. Remarks on Some Inequalities for Polynomials [PDF]

, 2013
MSC 2010: 30A10, 30C10, 30C80, 30D15, 41A17.In the present article, I point out serious errors in a paper published in Mathematica Balkanica three years ago. These errors seem to go unnoticed because some mathematicians are applying the results stated in
Hachani, M. A.
core  

Some exact Bernstein-Szegö inequalities on the standard triangle

, 2017
An actual problem in the theory of approximations is to extend the univariate inequality of Bernstein to the multivariate setting. This question is satisfactorily settled in the case of a centrally symmetric convex body.
L. Milev, N. Naidenov
semanticscholar   +1 more source

Principles of Extremum and Application to some Problems of Analysis [PDF]

, 1998
AMS subject classification: 41A17, 41A50, 49Kxx, 90C25.The aim of this paper is to demonstrate applications of a direct approach to the solution of extremal problems to some concrete problems of classical analysis, calculus of variations and ...
Tikhomirov, V.
core  

Pointwise Approximation Theorems for Combinations of Bernstein Polynomials With Inner Singularities

, 2010
We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.Comment: 13 pages ...
Lu, Wen-Ming, Zhang, Lin
core   +1 more source

On constrained Markov-Nikolskii type inequality for $k-$absolutely monotone polynomials [PDF]

, 2016
We consider the classical problem of estimating norms of higher order derivatives of algebraic polynomial via the norms of polynomial itself. The corresponding extremal problem for general polynomials in uniform norm was solved by A. A. Markov. In $1926,$
Klurman, Oleksiy
core  

New moduli of smoothness

, 2014
In this paper, we discuss various properties of the new modulus of smoothness \[ \omega^\varphi_{k,r}(f^{(r)},t)_p := \sup_{0 < h\leq t}\|\mathcal W^r_{kh}(\cdot) \Delta_{h\varphi(\cdot)}^k (f^{(r)},\cdot)\|_{L_p[-1,1]}, \] where $\mathcal W_\delta(x) = \
Kopotun, K. A., Leviatan, D., Shevchuk, I. A.   +2 more
core   +1 more source

Inequalities for Lorentz polynomials [PDF]

, 2014
We prove a few interesting inequalities for Lorentz polynomials including Nikolskii-type inequalities. A highlight of the paper is a sharp Markov-type inequality for polynomials of degree at most n with real coefficients and with derivative not vanishing
Erdelyi, Tamas
core   +2 more sources

Polynomial estimates, exponential curves and Diophantine approximation

, 2010
Let $\alpha\in(0,1)\setminus{\Bbb Q}$ and $K=\{(e^z,e^{\alpha z}):\,|z|\leq1\}\subset{\Bbb C}^2$. If $P$ is a polynomial of degree $n$ in ${\Bbb C}^2$, normalized by $\|P\|_K=1$, we obtain sharp estimates for $\|P\|_{\Delta^2}$ in terms of $n$, where ...
Coman, Dan, Poletsky, Evgeny A.
core   +1 more source