arXiv subjects

Malik Saad Al-Muhja

Publications and source records attributed to Malik Saad Al-Muhja.

3 recordsLinked to original sources

arXiv2020

Equivalence of Weighted DT-Moduli of (Co)convex Functions

The paper present new definitions for weighted DT moduli. Similarly, we a general outcome in an equivalence of moduli of smoothness are obtained. It is known that, any $r \in \mathbb{N}_{\circ}$ , $0<p \leq \infty$, $1 \leq η\leq r$ and $ϕ(x)=\sqrt{1-x^2}$, the inequalities $ω^ϕ_{i+1,r} \; (f^{(r)}, \| θ_{\mathcal{N}} \|)_{w_{α, β}, p} \sim ω^ϕ_{i,r+1} \; (f^{(r+1)}, \| θ_{\mathcal{N}} \|)_{w_{α, β}, p}$ and $ω^ϕ_{i+η} \; (f, \| θ_{\mathcal{N}} \|)_{α, β, p} \sim \| θ_{\mathcal{N}} \|^{- η} ω^ϕ_{i, 2 η} \; (f^{(2 η)}, \| θ_{\mathcal{N}} \|)_{α+ η, β+ η, p}$ are valid.

math.FA↗

arXiv2020

Derivation of new Degrees for Best (Co)convex and Unconstrained Polynomial Approximation in $\mathbb{L}^{α, β}_p$ space: I

The purpose of this work is to present the derivation and an estimate of the degrees of the best approximation based on convex, coconvex and unconstrained polynomials, and discuss some applications. We simplify the term convex and coconvex polynomial as (co)convex polynomial herein.

math.FA↗

arXiv2020

On Extend the Domain of (Co)convex Polynomial

We will use different way (in this work) from the existing methods in the literature which speaking in the separation of convex sets was carried out by hyperplanes. We are examining the behavior of convex set which is the domain of convex and coconvex polynomial. We simplify this term as (co)convex polynomial herein.

math.FA↗