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We study a Kantorovich-type modification of the operators introduced in [1] and we characterize their convergence in the $L^{p}$ -norm. We also furnish a quantitative estimate of the convergence.

$L_{p}$ inequalities for the growth of polynomials with restricted zeros

Nisar A. Rather, Suhail Gulzar, Aijaz A. Bhat (2022)

Archivum Mathematicum

Let $P (z) = \sum_{ν = 0}^{n} a_{ν} z^{ν}$ be a polynomial of degree at most $n$ which does not vanish in the disk $| z | < 1$ , then for $1 \leq p < \infty$ and $R > 1$ , Boas and Rahman proved ${∥P (R z)∥}_{p} \leq ({∥R^{n} + z∥}_{p} / {∥1 + z∥}_{p}) {∥P∥}_{p} .$ In this paper, we improve the above inequality for $0 \leq p < \infty$ by involving some of the coefficients of the polynomial $P (z)$ . Analogous result for the class of polynomials $P (z)$ having no zero in $| z | > 1$ is also given.

$L_{p}$ inequalities for the polar derivative of a polynomial.

Rather, Nisar A. (2008)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

$L_{p}$ -inverse theorem for modified beta operators.

Gupta, Vijay, Maheshwari, Prerna, Jain, V. K. (2003)

International Journal of Mathematics and Mathematical Sciences

$L^{p}$ norm convergence of rational operators on the unit circle.

Szabó, Zoltán (1998)

Mathematica Pannonica

L1-Approximation to Zero.

Jens Fromm (1976)

Mathematische Zeitschrift

L1-Approximation verallgemeinerter konvexer Funktionen durch Splines mit freien Knoten.

Kurt Jetter (1978/1979)

Mathematische Zeitschrift

L2-approximation by the translates of a function and related attenuation factors.

S.L. Lee, Roger C.E. Tan, W.S. Tang (1991/1992)

Numerische Mathematik

La Fonctionnelle g Et Queloques Problèmes Des Meilleures Approximations Dans Des Espaces Normés

P. M. Miličić (1990)

Publications de l'Institut Mathématique

La Formula De Simpson Tridimensional.

Gabriel Poveda Ramos (1987)

Revista colombiana de matematicas

Lacunary equi-statistical convergence of positive linear operators

Hüseyin Aktuğlu, Halil Gezer (2009)

Open Mathematics

In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation...

Lagrange interpolation and entire functions

Radwan Al-Jarrah, Kamel Al-Khaled (1990)

Revista colombiana de matematicas

Lagrange multipliers for higher order elliptic operators

Carlos Zuppa (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, the Babuška’s theory of Lagrange multipliers is extended to higher order elliptic Dirichlet problems. The resulting variational formulation provides an efficient numerical squeme in meshless methods for the approximation of elliptic problems with essential boundary conditions.

Lagrange multipliers for higher order elliptic operators

Carlos Zuppa (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, the Babuška's theory of Lagrange multipliers is extended to higher order elliptic Dirichlet problems. The resulting variational formulation provides an efficient numerical squeme in meshless methods for the approximation of elliptic problems with essential boundary conditions.

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