@Article{ATA-30-205,
author = {X. R. Yang, C. G. Zhang and Y. D. Ma},
title = {Approximation of Generalized Bernstein Operators},
journal = {Analysis in Theory and Applications},
year = {2014},
volume = {30},
number = {2},
pages = {205--213},
abstract = {<p style="text-align: justify;">This paper is devoted to studying direct and converse approximation theorems of the generalized Bernstein operators $C_{n}(f,s_{n},x)$ via so-called unified modulus$\omega_{\varphi^{\lambda}}^{2}(f,t)$, $0\leq\lambda\leq1$. We obtain &nbsp;main results as follows$$ \omega_{\varphi^{\lambda}}^{2}(f,t)=O(t^{\alpha})\Longleftrightarrow|C_{n}(f,s_{n},x)-f(x)|=\mathcal{O}\big((n^{-\frac{1}{2}}\delta_{n}^{1-\lambda}(x))^{\alpha}\big),$$where $\delta_{n}^{2}(x)=\max\{\varphi^{2}(x),{1}/{n}\}$ and $0&lt;\alpha&lt;2$.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2014.v30.n2.6},
url = {http://global-sci.org/intro/article_detail/ata/4485.html}
}