EQUIVALENCE OF WEIGHTED DT-MODULI
OF CONVEX FUNCTIONS
Malik Saad Al-Muhja1,2, Habibulla Akhadkulov1
Nazihah Ahmad1
1Department of Mathematics and Statistics
School of Quantitative Sciences
College of Arts and Sciences, Universiti Utara Malaysia
06010 Sintok, Kedah, MALAYSIA
2 Department of Mathematics and Computer Application
College of Sciences, University of Al-Muthanna
Samawa 66001, IRAQ

Abstract

This work present a new conclusion for weighted DT-moduli of smoothness (DTMS). Furthermore, the best weighted approximation on a finite closed interval $\mathbb{D} = [-1,1]$ are computed by DTMS. For any $r \in \mathbb{N}_{\circ}$, $0< p \leq \infty$, $1\leq \eta \leq r$ and $\phi (x) = \sqrt{1 - x^{2}}$, the equivalences \begin{equation*} \mathcal{E}^{(2)}_{n} (f, w_{\alpha, \beta})_{p} \sim \varpi^... ...a_{\mathcal{N}} \Vert, \mathbb{D})_{w_{\alpha, \beta}, p} % \sim \end{equation*} \begin{equation*} \sim \, \varpi^{\phi}_{i+1,r-1} \; (f^{(r)}, \Vert \theta_{\m... ...rt, \mathbb{D})_{w_{\alpha+ \frac{1}{2}, \beta+ \frac{1}{2}}, p} \end{equation*} and \begin{equation*} \mathcal{E}^{(2)}_{n} (f, w_{\alpha, \beta})_{p} \sim \varpi^... ...lpha, \beta, p} \sim \Vert \theta_{\mathcal{N}} \Vert^{- \eta} % \end{equation*} \begin{equation*} \times\, \varpi^{\phi}_{i, 2 \eta} \; (f^{(2 \eta)}, \Vert \theta_{\mathcal{N}} \Vert)_{\alpha+ \eta, \beta+ \eta, p} \end{equation*} are valid.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 4
Year: 2021

DOI: 10.12732/ijam.v34i4.2

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