Negative theorems for co-positive Lp1, 0< p < 1 interpolating approximation

Dreeb, Nabiha Kahtan; Bhaya, Eman Samir

doi:10.47974/JIM-2547

Open Access Research Article

Negative theorems for co-positive Lp1, 0< p < 1 interpolating approximation

^*Nabiha Kahtan DreebCorresponding authornabihakahtan@gmail.comDepartment of Mathematics College of Education for Pure Sciences University of BabylonBabylon, 51002, IraqView full profile → , Eman Samir Bhayaemanbhaya@alzahraa.edu.iqDepartment of Mathematics College of Education Al-Zahraa University for WomenKarbala, IraqView full profile →

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pp. 1551–1558Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2547XML

Received:: 01 Nov 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2547
Pages:: 1551–1558

Abstract

This work provides a rigorous mathematical analysis of the relationship between Hermite interpolation and function approximation, such that at a certain point Aq ∈ 𝔸q, where 𝔸q, is the set of all collections Aq := {αi}qi=1 of points αi such that –1 ≤ αq < ⋯ < α1 ≤ 1, q ∈ N. Approximation polynomials (if possible) must interpolate the function and its derivatives, where at such points the function value matches not only the polynomial but also its derivatives. This kind of interpolation is known as Hermite interpolation also investigates whether the interpolation conditions can be extended to derivatives of the functionf. The accuracy of approximation does not just rely on the smoothness of f, but also the location points of interpolation, such that the points in Aq lie in the interior of the interval I = [–1, 1] or on the boundary of interval I, and so depend on the odd or even for highest derivatives for the f. With the points from Ys ∈ 𝕐s, where 𝕐s a sets for every collection Ys := {yi}si=1 for the point yi, such that –1 < ys < ⋯

Keywords

Positive approximation Co-positive approximation Constrained approximation Pointwise approximation

Subject Classifications

Primary 93A30Secondary 49K15

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