Cesàro summability of lagrange interpolation on Jacobi roots

2004 ◽  
Vol 41 (4) ◽  
pp. 437-451
Author(s):  
L. Szili
Keyword(s):  
Lagrange Interpolation ◽  
Function Spaces ◽  
Cesàro Means ◽  
Cesàro Summability ◽  
Weighted Function ◽  
Weighted Function Spaces ◽  
Cesaro Means ◽  
Cesaro Summability ◽  
Cesáro Means ◽  
Uniformly Convergent

The aim of this paper is to give such weighted function spaces in which the sequence of Cesàro means of Lagrange interpolatory polynomials on Jacobi roots are uniformly convergent.

scholarly journals Lebesgue points of $$\ell _1$$-Cesàro summability of d-dimensional Fourier series

2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
Lebesgue Point ◽  
Cesàro Means ◽  
Cesàro Summability ◽  
Cesaro Means ◽  
Cesaro Summability ◽  
Lebesgue Points ◽  
Cesáro Means

AbstractWe generalize the classical Lebesgue’s theorem and prove that the $$\ell _1$$ ℓ 1 -Cesàro means of the Fourier series of the multi-dimensional function $$f\in L_1({{\mathbb {T}}}^d)$$ f ∈ L 1 ( T d ) converge to f at each strong $$\omega $$ ω -Lebesgue point.

scholarly journals Hermite-Fejér and Grünwald interpolation at generalized Laguerre zeros

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4855-4863
Author(s):  
Bonis De ◽  
David Kubayi
Keyword(s):  
Laguerre Polynomials ◽  
Function Spaces ◽  
Weighted Function ◽  
Weighted Function Spaces ◽  
Generalized Laguerre Polynomials ◽  
Uniformly Convergent

We introduce special Hermite-Fej?r and Gr?nwald operators at the zeros of the generalized Laguerre polynomials. We will prove that these interpolation processes are uniformly convergent in suitable weighted function spaces.

scholarly journals Linear Differential Equations on Some Classes of Weighted Function Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1113
Author(s):  
Ahmed El-Sayed Ahmed ◽  
Amnah E. Shammaky
Keyword(s):  
Specific Growth ◽  
Function Spaces ◽  
Entire Solutions ◽  
Linear Type ◽  
Weighted Function ◽  
Weighted Function Spaces ◽  
Type Classes ◽  
Type Differential Equation ◽  
Linear Differential ◽  
Weighted Type

Some weighted-type classes of holomorphic function spaces were introduced in the current study. Moreover, as an application of the new defined classes, the specific growth of certain entire-solutions of a linear-type differential equation by the use of concerned coefficients of certain analytic-type functions, that is the equation h(k)+Kk−1(υ)h(k−1)+…+K1(υ)h′+K0(υ)h=0, will be discussed in this current research, whereas the considered coefficients K0(υ),…,Kk−1(υ) are holomorphic in the disc ΓR={υ∈C:|υ|<R},0<R≤∞. In addition, some non-trivial specific examples are illustrated to clear the roles of the obtained results with some sharpness sense. Hence, the obtained results are strengthen to some previous interesting results from the literature.

Growth conditions on Cesàro means of higher order

2013 ◽  
Vol 79 (3-4) ◽  
pp. 545-581
Author(s):  
Laurian Suciu ◽  
Jaroslav Zemánek
Keyword(s):  
Growth Conditions ◽  
Higher Order ◽  
Cesàro Means ◽  
Cesaro Means ◽  
Cesáro Means
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