A Class of Birkhoff Type Interpolation and Applications

2018 ◽  
Vol 73 (1) ◽  
Author(s):  
A. Mahmoodi ◽  
A. Nazarzadeh
Keyword(s):  
Type Interpolation

scholarly journals On Hermite-Fejér type interpolation on the Chebyshev nodes

1993 ◽  
Vol 47 (1) ◽  
pp. 13-24 ◽  
Author(s):  
Graeme J. Byrne ◽  
T.M. Mills ◽  
Simon J. Smith
Keyword(s):  
Approximation Error ◽  
Interpolation Polynomial ◽  
Precise Estimate ◽  
Type Interpolation ◽  
Interpolation Methods ◽  
Chebyshev Nodes ◽  
Interpolatory Process

Given f ∈ C [−1, 1], let Hn, 3(f, x) denote the (0,1,2) Hermite-Fejér interpolation polynomial of f based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |Hn, 3(f, x) − f(x)|. Further, we demonstrate a method of combining the divergent Lagrange and (0,1,2) interpolation methods on the Chebyshev nodes to obtain a convergent rational interpolatory process.

scholarly journals On Hermite-Fejér type interpolation

1983 ◽  
Vol 28 (1) ◽  
pp. 39-51 ◽  
Author(s):  
H.-B. Knoop ◽  
B. Stockenberg
Keyword(s):  
Jacobi Polynomial ◽  
Higher Order ◽  
Interpolation Operator ◽  
Type Interpolation

For the Hermite-Fejér interpolation operator of higher order constructed on the roots , 1 ≤ k ≤ m, of the Jacobi-polynomial it is shown that is positive for all m ∈ N, if (α, β) ∈ [−¾, −¼]2. Further there is given an bound, which implies for arbitrary f ∈ C(I) and (α, β) ∈ [−¾, −¼]2.

On Ingham-type interpolation in

2010 ◽  
Vol 348 (13-14) ◽  
pp. 807-810 ◽  
Author(s):  
Alexander Olevskii ◽  
Alexander Ulanovskii
Keyword(s):  
Type Interpolation

scholarly journals Hermite-Fejér type interpolation and Korovkin's theorem

1990 ◽  
Vol 42 (3) ◽  
pp. 383-390
Author(s):  
H.-B. Knoop ◽  
F. Locher
Keyword(s):  
Uniform Convergence ◽  
Jacobi Polynomials ◽  
Korovkin Theorem ◽  
Type Interpolation ◽  
Special Values ◽  
Convergence Results ◽  
Interpolation Operators ◽  
Positive Functionals ◽  
Interpolation Polynomials ◽  
Korovkin’S Theorem

In this note we consider Hermite-Fejér interpolation at the zeros of Jacobi polynomials and with additional boundary conditions. For the associated Hermite-Fejér type operators and special values of α, β it was proved by the first author in recent papers that one has uniform convergence on the whole interval [−1,1]. The second author could show by introducing the concept of asymptotic positivity how to get the known convergence results for the classical Hermite-Fejér interpolation operators. In the present paper we show, using a slightly modified Bohman-Korovkin theorem for asymptotically positive functionals, that the Hermite-Fejér type interpolation polynomials , converge pointwise to f for arbitrary α, β > −1. The convergence is uniform on [−1 + δ,1 − δ].

Hermite-type interpolation of squared-magnitude functions

1991 ◽  
Vol 43 (3) ◽  
pp. 265-270 ◽  
Author(s):  
A. Lepschy ◽  
G.A. Mian ◽  
U. Viaro
Keyword(s):  
Type Interpolation

scholarly journals Atomic decompositions of Lorentz martingale spaces and applications

2009 ◽  
Vol 7 (2) ◽  
pp. 153-166 ◽  
Author(s):  
Jiao Yong ◽  
Peng Lihua ◽  
Liu Peide
Keyword(s):  
Atomic Decomposition ◽  
Weak Type ◽  
Interpolation Theorem ◽  
Sublinear Operator ◽  
Sufficient Condition ◽  
Atomic Decompositions ◽  
Type Interpolation ◽  
Marcinkiewicz Interpolation Theorem ◽  
Decomposition Theorems

In the paper we present three atomic decomposition theorems of Lorentz martingale spaces. With the help of atomic decomposition we obtain a sufficient condition for sublinear operator defined on Lorentz martingale spaces to be bounded. Using this sufficient condition, we investigate some inequalities on Lorentz martingale spaces. Finally we discuss the restricted weak-type interpolation, and prove the classical Marcinkiewicz interpolation theorem in the martingale setting.

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