A method of summability of Lagrange interpolation

Mache, Detlef H.

doi:10.1155/s0161171294000037

Cited by 6 publications

(2 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Starting from [2], for example, variations on the following question have been addressed (see, e.g., [4,17]): For each n # N, can one construct a positive-preserving interpolation operator, L n , such that…”

Section: Introduction Let (X And} And)=(c[a B] and }And ) Wherementioning

confidence: 99%

On j-Convex Preserving Interpolation Operators

Prophet

2000

Journal of Approximation Theory

View full text Add to dashboard Cite

We present results regarding the existence of j-convex preserving interpolation operators, as well as results concerning the determination of existence of such operators. We include an application in which we make use of a sufficient set of testfunctions to characterize when every degree of convexity can be preserved among particular families of polynomial interpolation operators, which include the Bernstein operators. Academic Press

show abstract

Section: Introduction Let (X And} And)=(c[a B] and }And ) Wherementioning

confidence: 99%

On j-Convex Preserving Interpolation Operators

Prophet

2000

Journal of Approximation Theory

View full text Add to dashboard Cite

show abstract

“…Other solutions for Butzer's problem are presented in [5]. However, some summability methods for Lagrange interpolntion (see [11], [10]) furnish us nlso an affirmative answer to the question raised in [2]..…”

mentioning

confidence: 99%

The Θ‐transformation of certain positive linear operators

Lupa¹,

Mache²

1994

International Journal of Mathematics and Mathematical Sciences

Self Cite

View full text Add to dashboard Cite

ABSTRACT. The intention of this paper is to describe a const,'uction method for a new sequence of linear positive operators, which enables us to get a pointwise order of approximation regarding the polynomial sun'tmator operators which have "best" properties of approximation.KEY WORDS AND PHRASES. Approximation by positive linear operators, discrete linear operators, (C, 1) means of Chebyshev series.1. The aim of this paper can be described in the following way" Starting wih a sequence A (A,) of approximation operators, we construct by means of the so called 0 transformation a new sequence of operators B (B=) O(A). With the known properties of A we get the corresponding properties of the sequence B O(A). We also prove, that if A is the sequence of (C, 1) means of Chebyshev series, the polynomials (Bf), f C(I), furnish a pointwise order of approximation similar to the best order of approximation.Let H,, n 0, be the linear space of all algebraic polynomials with real coefficients of degree 5 n and T,(t) cos(, arccos t) the n th Chebyshev polynomial, n 0. Further for f X and a polynomial 9 we use the inner product

show abstract

Best direct and converse results for Lagrange-type operators

Mache

1995

Approx. Theory & its Appl.

View full text Add to dashboard Cite

A method of summability of Lagrange interpolation

Abstract: ABSTRACT. The author uses in this paper a technique fi'om numerical integration (see [9]

Cited by 6 publications

References 5 publications

On j-Convex Preserving Interpolation Operators

On j-Convex Preserving Interpolation Operators

The Θ‐transformation of certain positive linear operators

Best direct and converse results for Lagrange-type operators

Contact Info

Product

Resources

About